Download App

Maths M.C.Q (1 Marks)

Mathematical Reasoning · CBSE STD 11 Science (CBSE - English Medium). 180 questions.

Questions

M.C.Q (1 Marks)

Take a timed test

180 questions · auto-graded multiple-choice test.

MCQ 11 Mark
If the truth value of the statement $p \rightarrow (\sim q ∨ r)$ is false $(F),$ then the truth values of the statements $p, q, r$ are respectively.
  • ✓
    $\text{T, T, F}$
  • B
    $\text{T, F, F}$
  • C
    $\text{T, F, T}$
  • D
    $\text{F, T, T}$
Answer
Correct option: A.
$\text{T, T, F}$
View full question & answer→
MCQ 21 Mark
Choose the correct answer : The negation of the statement “The product of $3$ and $4$ is $9”$ is.
  • ✓
    It is false that the product of $3$ and $4$ is $9.$
  • B
    The product of $3$ and $4$ is $12.$
  • C
    The product of $3$ and $4$ is not $12$.
  • D
    It is false that the product of $3$ and $4$ is not $9.$
Answer
Correct option: A.
It is false that the product of $3$ and $4$ is $9.$
The negation of the statement is “It is false that the product of $3$ and $4$ is $9”.$
View full question & answer→
MCQ 31 Mark
Write the inverse of the statement: If you do not drink your milk, you will not be strong.
  • A
    If you are strong, then you drink your milk,
  • B
    If you do not drink your milk, then you are strong.
  • ✓
    If you drink your milk, then you are strong.
  • D
    None of the above.
Answer
Correct option: C.
If you drink your milk, then you are strong.
If you drink your milk is negation of the hypothesis if you donot drink your milk you are strong is negation of the conclusion you will not be strong.
View full question & answer→
MCQ 41 Mark
The converse of: "If two triangles are congruent then they are similar" is:
  • ✓
    If two triangles are similar then they are congruent.
  • B
    If two triangles are not congruent then they are not similar.
  • C
    If two triangles are not similar then they are not congruent.
  • D
    None.
Answer
Correct option: A.
If two triangles are similar then they are congruent.
The converse of $"$ If $P$ then $Q"$ is $"$ If $Q$ then $P".$
View full question & answer→
MCQ 51 Mark
If statement p → (q∨r) is true then the truth values of statements p, q, r respectively:
  • A
    T, F, T
  • B
    F, T, F
  • C
    F, F, F
  • ✓
    all of these
Answer
Correct option: D.
all of these
d. all of these
Solution:
$\because$ p → (q∨r) is false
⇒ p is true and (q ∨ r) is false
⇒ p is true, q and r both are false
i.e. p → (q ∨ r) is false when truth values of p, q, r are T, F, F respectively otherwise it is true.
View full question & answer→
MCQ 61 Mark
Which of the following is not a statement.
  • A
    $8$ is less than $6.$
  • B
    Every set is finite set.
  • C
    The sun is a star.
  • ✓
    Mathematics is fun.
Answer
Correct option: D.
Mathematics is fun.
$8$ is less than $6$ if false.
So it is a statement.
Every set is finite set is false.
So it is a statement.
The sun is a star is true.
So it is a statement.
Mathematics is fun.
This sentence is not always true.
Hence, it is not a statement
View full question & answer→
MCQ 71 Mark
Which of the following is contrapositive of “If $x$ is divisible by $4$ then $x$ must be divisible by $2”\ ?$
  • A
    If $x$ is divisible by $2$ then $x$ must be divisible by $4$
  • B
    If $x$ is not divisible by $2$ then $x$ must be divisible by $4$
  • ✓
    If $x$ is not divisible by $2$ then $x$ is not divisible by $4$
  • D
    If $x$ is divisible by $4$ then $x$ is not divisible by $2$
Answer
Correct option: C.
If $x$ is not divisible by $2$ then $x$ is not divisible by $4$
Contrapositive statement for given statement $“$ if $p$ then $q”$ is $“$ if not $q$ then not $p”$
i.e. $\sim q \Rightarrow \sim p.$
So, contrapositive for $“$ If $x$ is divisible by $4$ then $x$ must be divisible by $2”$ is $“$ If $x$ is not divisible by $2$ then $x$ is not divisible by $4”.$
View full question & answer→
MCQ 81 Mark
$\sim (p \rightarrow q) \rightarrow [(\sim p) ∨ (\sim q)]$ is.
  • ✓
    a tautology
  • B
    a contradiction
  • C
    neither a tautology nor contradiction
  • D
    cannot come any conclusion
Answer
Correct option: A.
a tautology
View full question & answer→
MCQ 91 Mark
If $(p$ or $q)$ is true, then:
  • A
    $p$ is true and $q$ is false
  • B
    $p$ is true and $q$ is true
  • C
    $p$ is false and $q$ is true
  • ✓
    All of the above
Answer
Correct option: D.
All of the above
$(p$ or $q)$ is false when both $p$ and $q$ are false otherwise it is true.
View full question & answer→
MCQ 101 Mark
Which of the following is a statement.
  • A
    I will go tomorrow
  • B
    She will come today
  • ✓
    $3$ is a prime number
  • D
    Tomorrow is Friday
Answer
Correct option: C.
$3$ is a prime number
The statement $3$ is a prime number is true.
So, it is a statement.
View full question & answer→
MCQ 111 Mark
If $p, q, r$ are statement with truth values $\text{F, T, F}$ respectively then the truth value of $(\sim p \rightarrow \sim q) ∨, r$ is.
  • A
    true
  • ✓
    false
  • C
    false if $r$ is true
  • D
    false if $q$ is false
Answer
Correct option: B.
false
View full question & answer→
MCQ 121 Mark
Which of the following is a statement?
  • A
    Close the door
  • ✓
    $11$ comes after $12$
  • C
    India is a beautiful country
  • D
    This is useless
Answer
Correct option: B.
$11$ comes after $12$
$“$Close the door$”$ is not a statement as it is an imperative sentence.
$“11$ comes after $12”$ is a statement as it is true.
$“$India is a beautiful country$”$ is not a statement as opinion of beautifulness vary from person to person.
$“$This is useless$”$ is not a statement as it involves this which doesn’t give any idea about what we are talking.
View full question & answer→
MCQ 131 Mark
Choose the correct answer: The negation of the statement.
$“101$ is not a multiple of $3”$ is.
  • ✓
    $101$ is a multiple of $3.$
  • B
    $101$ is a multiple of $2.$
  • C
    $101$ is an odd number.
  • D
    $101$ is an even number.
Answer
Correct option: A.
$101$ is a multiple of $3.$
Let $p: 101$ is not multiple of $3.$
$\sim p: 101$ is a multiple of $3.$
View full question & answer→
MCQ 141 Mark
The contrapositive of $(p ∨ q) \rightarrow r$ is.
  • A
    $\sim r \rightarrow (p ∧ q)$
  • B
    $\sim r \rightarrow \sim (p ∨ q)$
  • ✓
    $p \rightarrow (p ∧ q)$
  • D
    $\sim r \rightarrow (\sim p\ ∧ \sim q)$
Answer
Correct option: C.
$p \rightarrow (p ∧ q)$
View full question & answer→
MCQ 151 Mark
If $(p$ and $q)$ is false then.
  • A
    $p$ is true and $q$ is false
  • B
    $p$ is false and $q$ is false
  • C
    $p$ is false and $q$ is true
  • ✓
    All of the above
Answer
Correct option: D.
All of the above
$(p$ and $q)$ is true when both $p$ and $q$ are true otherwise it is false.
View full question & answer→
MCQ 161 Mark
If the standard deviation of a data is $820$ and mean of the data is $50,$ find the coefficient of variation.
  • ✓
    $16.4$
  • B
    $164$
  • C
    $1640$
  • D
    $1.64$
Answer
Correct option: A.
$16.4$
Coefficient of Variance $= (\frac{\text{Standard Deviation}}{\text{Mean}}) \times 100$
$\Rightarrow \text{ Coefficient of Variance} = (\frac{820}{50}) \times 100 = 16.4.$
View full question & answer→
MCQ 171 Mark
The negation of the compound statement $p ∨ (\sim p ∨ q)$ is.
  • A
    $(p ∧ q) ∨ p$
  • ✓
    $(p\ ∧ \sim q)\ ∧ \sim p$
  • C
    $(p\ ∧ \sim q) ∨\ p$
  • D
    $(p\ ∧ \sim q)\ ∨ \sim p$
Answer
Correct option: B.
$(p\ ∧ \sim q)\ ∧ \sim p$
View full question & answer→
MCQ 181 Mark
What is converse for statement if $p$ then $q?$
  • A
    If not $q$ then not $p$
  • ✓
    If $q$ then $p$
  • C
    If not $p$ then $q$
  • D
    If not $p$ then not $q$
Answer
Correct option: B.
If $q$ then $p$
Converse statement for given statement $“$ if $p$ then $q”$ is $“$ if $q$ then $p”$
i.e. $q \Rightarrow p$ or $q$ implies $p.$
View full question & answer→
MCQ 191 Mark
The false statement in the following is.
  • A
    $p Λ (~p)$ is contradiction
  • ✓
    $(p \Rightarrow q) = (~q \Rightarrow ~p)$ is a contradiction
  • C
    $~(~p) = p$ is a tautology
  • D
    $p ∨ (~p) =$ is a tautology
Answer
Correct option: B.
$(p \Rightarrow q) = (~q \Rightarrow ~p)$ is a contradiction
$(p \Rightarrow q) = (~q \Rightarrow ~p)$ is a contradiction
View full question & answer→
MCQ 201 Mark
Choose the correct answer : Which of the following is the conditional $p \rightarrow q?$
  • A
    $q$ is sufficient for $p.$
  • B
    $p$ is necessary for $q.$
  • ✓
    $p$ only if $q.$
  • D
    if $q,$ then $p.$
Answer
Correct option: C.
$p$ only if $q.$
We know that $p \rightarrow q$ is same as $p$ only if $q.$
View full question & answer→
MCQ 211 Mark
Choose the correct answer: Which of the following is a statement.
  • A
    $x$ is a real number.
  • B
    Switch off the fan.
  • ✓
    $6$ is a natural number.
  • D
    Let me go.
Answer
Correct option: C.
$6$ is a natural number.
Since, statement is a sentence which is ether true or false.
So, $6$ is a natural number which is true.
View full question & answer→
MCQ 221 Mark
Choose the correct answer:
The negation of the statement.
$“72$ is divisible by $2$ and $3”$ is.
  • ✓
    $72$ is not divisible by $2$ or $72$ is not divisible by $3.$
  • B
    $72$ is not divisible by $2$ and $72$ is not divisible by $3.$
  • C
    $72$ is divisible by $2$ and $72$ is not divisible by $3.$
  • D
    $72$ is not divisible by $2$ and $72$ is divisible by $3.$
Answer
Correct option: A.
$72$ is not divisible by $2$ or $72$ is not divisible by $3.$
We have, $p: 72$ is divisible by $2$ and $3.$
Let $q: 72$ is divisible by $2.$
$r: 72$ is divisible by $3.$
$\sim q: 72$ is not divisible by $2.$
$\sim r. 72$ is not divisible by $3.$
$\sim (q ⋀ f ) -\sim q v \sim r$
$\Rightarrow 72$ is not divisible by $2$ or $72$ is not divisible by $3.$
View full question & answer→
MCQ 231 Mark
If $p \Rightarrow (q ∨ r)$ is false, then the truth values of $p, q, r$ are respectively $\sim .$
  • A
    $\text{F, T, T}$
  • ✓
    $\text{T, F, F}$
  • C
    $\text{T, T, F}$
  • D
    $\text{F, F, F}$
Answer
Correct option: B.
$\text{T, F, F}$
View full question & answer→
MCQ 241 Mark
Which of the following is the conditional $p \rightarrow q.$
  • A
    $q$ is sufficient for $p$
  • B
    $p$ is necessary for $q$
  • ✓
    $p$ only if $q$
  • D
    If $q$ then $p$
Answer
Correct option: C.
$p$ only if $q$
Given, $p \rightarrow q$
Now, conditional of the statement is
$p$ only if $q$
View full question & answer→
MCQ 251 Mark
The negation of the Boolean expression $p ∨ (\sim p ∧ q)$ is equivalent to $\sim .$
  • A
    $p\ ∧ \sim q$
  • ✓
    $\sim p ∧ q$
  • C
    $\sim p\ ∨ \sim q$
  • D
    $\sim p ∨ q$
Answer
Correct option: B.
$\sim p ∧ q$
View full question & answer→
MCQ 261 Mark
Logical equivalent proposition to the proposition $\sim (p ∨ q)$ is.
  • A
    $\sim p \rightarrow q$
  • ✓
    $\sim p\ ∧ \sim q$
  • C
    $\sim p\ ∨ \sim q$
  • D
    $\sim p \rightarrow \sim q$
Answer
Correct option: B.
$\sim p\ ∧ \sim q$
View full question & answer→
MCQ 271 Mark
$............$ statement is made up of two or more statements where each statement is known as $............$ statement.
  • A
    Compound, compound
  • ✓
    Compound, component
  • C
    Component, compound
  • D
    Component, component
Answer
Correct option: B.
Compound, component
A compound statement is made up of two or more statements where each statement is known as component statement.
View full question & answer→
MCQ 281 Mark
Which of the following is a compound statement.
  • A
    Sun is a star
  • B
    I am a very strong boy
  • C
    There is something wrong in the room
  • ✓
    $7$ is both odd and prime number.
Answer
Correct option: D.
$7$ is both odd and prime number.
A compound statement is connected with And, or, etc.
So, the statement $7$ is both odd and prime number is a compound statement.
View full question & answer→
MCQ 291 Mark
Which of the following is the inverse of the proposition $"$If a number is prime, then it is odd$"$?
  • A
    If a number is not prime, then it is odd.
  • ✓
    If a number is not a prime, then it is not odd.
  • C
    If a number is not odd, then it is not a prime.
  • D
    If a number is not odd, then it is a prime.
Answer
Correct option: B.
If a number is not a prime, then it is not odd.
$p :$ A number is prime
$q :$ It is odd
We have $p \rightarrow q$
The inverse of $p \rightarrow q$ is $\sim p \rightarrow \sim q$
i.e. If a number is not a prime then it is not odd.
View full question & answer→
MCQ 301 Mark
Which of the following statements is a conjunction?
  • A
    Ram and Shyam are friends.
  • B
    Both Ram and Shyam are tall.
  • C
    Both Ram and Shyam are enemies.
  • ✓
    None of the above
Answer
Correct option: D.
None of the above
When the word connects two statements and we call the combined statement conjunction.
None of the statements is connected by and from the given.
View full question & answer→
MCQ 311 Mark
Choose the correct answer : The statement “If $x^2$ is not even, then x is not even” is converse of the statement.
  • A
    If $x^2$ is odd, then $x$ is even.
  • ✓
    If $x$ is not even, then $x^2$ is not even.
  • C
    If $x$ is even, then $x^2$ is even.
  • D
    If $x$ is odd, then $x^2$ is even.
Answer
Correct option: B.
If $x$ is not even, then $x^2$ is not even.
Let $p: x^2$ is not even.
$q: x$ is not even.
So, the converse of the statement $p \rightarrow q $ is $q \rightarrow p$
i.e., If $x$ is not even, then $x^2$ is not even.
View full question & answer→
MCQ 321 Mark
Let p and q be two propositions. Then, the contrapositive of the implication p → q is.
  • A
    p → q
  • B
    p ↔ q
  • C
    ∼p → ∼q
  • ✓
    ∼q → ∼p
Answer
Correct option: D.
∼q → ∼p
d. ∼q → ∼p
View full question & answer→
MCQ 331 Mark
What is contrapositive for statement if $p$ then $q\ ?$
  • ✓
    if not $q$ then not $p$
  • B
    if $q$ then $p$
  • C
    if not $p$ then $q$
  • D
    if not $p$ then not $q$
Answer
Correct option: A.
if not $q$ then not $p$
Contrapositive statement for given statement $“$ if $p$ then $q”$ is $“$ if not $q$ then not $p"$
i.e. $\sim q \Rightarrow \sim p.$
View full question & answer→
MCQ 341 Mark
If $p$ then $q$ means $............$ only if $............$
  • ✓
    $p, q$
  • B
    $q, p$
  • C
    $p, p$
  • D
    $q, q$
Answer
Correct option: A.
$p, q$
If $p$ then $q$ means $p$ only if $q$ or $p \Rightarrow q$ which is not same as $q$ only if $p$ or $q \Rightarrow p.$
View full question & answer→
MCQ 351 Mark
If $p$ then $q$ means $............$ implies $............$
  • A
    $q \Rightarrow p$
  • ✓
    $\sim q \Rightarrow \sim p$
  • C
    $~p \Rightarrow ~q$
  • D
    $p \Rightarrow ~q$
Answer
Correct option: B.
$\sim q \Rightarrow \sim p$
If $p$ then $q$ means $p \Rightarrow q$ or negation of $q$ implies negation of $p$
i.e. $\sim q \Rightarrow \sim p.$
View full question & answer→
MCQ 361 Mark
Consider the sentence: $x < 5$
Which of the following integers makes this open sentence true?
  • ✓
    $4$
  • B
    $5$
  • C
    $6$
  • D
    none of the above
Answer
Correct option: A.
$4$
Of the given options only $4 < 5,$
i.e; option $A$ satisfies $x < 5.$
View full question & answer→
MCQ 371 Mark
Which of the following is a statement?
  • ✓
    Roses are black.
  • B
    Mind your own business.
  • C
    Be punctual.
  • D
    Do not tell lies.
Answer
Correct option: A.
Roses are black.
The sentences in $(b), (c),$ and $(d)$ are neither true nor false.
All these sentences are pieces of advice.
Sentence $(a)$ is a definite statement.
View full question & answer→
MCQ 381 Mark
Which of the following is a statement?
  • A
    Rani is a beautiful girl.
  • B
    Shut the door.
  • C
    Yesterday was Friday.
  • ✓
    If its raining then there must be cloud in the sky.
Answer
Correct option: D.
If its raining then there must be cloud in the sky.
If its raining then there must be cloud in the sky.
This a statement.
A statement is a closed sentence.
It can also be a mathematical identity.
A statement should have a complete meaning independently.
View full question & answer→
MCQ 391 Mark
The negative of the statement "he is rich and happy" is given by:
  • A
    He is not rich and not happy.
  • ✓
    He is not rich or not happy.
  • C
    He is rich and happy.
  • D
    He is not rich and happy.
Answer
Correct option: B.
He is not rich or not happy.
The negation of the given statement is "he is not rich or not happy".
View full question & answer→
MCQ 401 Mark
Which of the following is true?
  • A
    Statements generally not use word like today and tomorrow
  • B
    Statements generally not use word like here and there
  • ✓
    Statements generally not use word like sum and product
  • D
    Statements generally not use word like this and that
Answer
Correct option: C.
Statements generally not use word like sum and product
Statements generally not use ambiguous words like here, there, this, that, today, tonight, tomorrow.
View full question & answer→
MCQ 411 Mark
Let $p, q, r$ be three statements such that the truth value of $(p ∧ q) \rightarrow (~q ∨ r)$ is $F.$ Then the truth values of $p, q, r$ are respectively $\sim .$
  • A
    $\text{T, F, T}$
  • B
    $\text{T, T, T}$
  • C
    $\text{F, T, F}$
  • ✓
    $\text{T, T, F}$
Answer
Correct option: D.
$\text{T, T, F}$
View full question & answer→
MCQ 421 Mark
The negation of the statement: "If I become a teacher, then I will open a school" is:
  • ✓
    I will become a teacher and I will not open a school.
  • B
    Either I will not become a teacher or I will not open a school.
  • C
    Neither I will become a teacher nor I will open a school.
  • D
    I will not become a teacher or I will open a school.
Answer
Correct option: A.
I will become a teacher and I will not open a school.
Let $p : I$ become a teacher
$q : I$ will open a school
The given statement is $p \rightarrow q = (\sim p)\ ∨ q$
It negation is $(p)\ ∨\ q) = p ∧ (q)$
Thus negation of the given statement is 'I will become a teacher and I will not open school'.
View full question & answer→
MCQ 431 Mark
Which of the following is contrapositive of $“$If $x$ is divisible by $4$ then $x$ must be divisible by $2”\ ?$
  • A
    If $x$ is divisible by $2$ then $x$ must be divisible by $4$
  • B
    If $x$ is not divisible by $2$ then $x$ must be divisible by $4$
  • ✓
    If $x$ is not divisible by $2$ then $x$ is not divisible by $4$
  • D
    If $x$ is divisible by $4$ then $x$ is not divisible by $2$
Answer
Correct option: C.
If $x$ is not divisible by $2$ then $x$ is not divisible by $4$
Contrapositive statement for given statement $“$if $p$ then $q”$ is $“$if not $q$ then not $p”$
i.e. $\sim q \Rightarrow \sim p.$
So, contrapositive for $“$If $x$ is divisible by $4$ then $x$ must be divisible by $2”$ is $“$If $x$ is not divisible by $2$ then $x$ is not divisible by $4”.$
View full question & answer→
MCQ 441 Mark
The denial of statement is called $...........$
  • ✓
    negation
  • B
    contradiction
  • C
    contrapositive
  • D
    compound
Answer
Correct option: A.
negation
The denial of statement is known as negation of the statement.
It is denoted by $\sim p$ if statement is denoted by $p.$
View full question & answer→
MCQ 451 Mark
If standard deviation of a data is $40$ and the coefficient of variation is $25600,$ then find the mean.
  • A
    $64$
  • ✓
    $6.4$
  • C
    $640$
  • D
    $0.64$
Answer
Correct option: B.
$6.4$
Coefficient of Variance $= (\frac{\text{Standard Deviation}}{\text{Mean}}) \times 100$
$\Rightarrow \text{ Mean} = \frac{\text{25600}}{4000} = 6.4.$
View full question & answer→
MCQ 461 Mark
Consider the statements:
$i.$ Two plus three is five.
$ii.$ Every square is a rectangle.
$iii.$ Sun rises in the east.
$iv.$ The earth is not a star.
Which of the above statements have truth value $(T)?$
  • A
    $(i)$ and $(ii)$
  • B
    $(ii)$ and $(iii)$
  • C
    $(iii)$ and $(iv)$
  • ✓
    All of these
Answer
Correct option: D.
All of these
We know, If a statement is true then its truth value is $T$ and if statement is false then $F.$
View full question & answer→
MCQ 471 Mark
In the truth table for the statement $\sim (\sim p\ ∨ \sim q)$, the last column has the truth value in the following order.
  • ✓
    $\text{T, F, F, F}$
  • B
    $\text{T, T, F, T}$
  • C
    $\text{F, T, T, F}$
  • D
    $\text{F, F, F, T}$
Answer
Correct option: A.
$\text{T, F, F, F}$
View full question & answer→
MCQ 481 Mark
In direct method to prove statement $“$If $p$ then $q”$ is valid or not, we assume $p$ to be $..........$ and prove $q$ to be $..........$
  • A
    true, false
  • ✓
    true, true
  • C
    false, false
  • D
    false, true
Answer
Correct option: B.
true, true
In direct method, we assume $p$ to be true and use it to prove that $q$ is also true.
There is no case for $p$ to be false in direct method.
View full question & answer→
MCQ 491 Mark
Which of the following is converse of $“$If $x$ is divisible by $4$ then $x$ must be divisible by $2”\ ?$
  • ✓
    If $x$ is divisible by $2$ then $x$ must be divisible by $4$
  • B
    If $x$ is not divisible by $2$ then $x$ must be divisible by $4$
  • C
    If $x$ is not divisible by $2$ then $x$ is not divisible by $4$
  • D
    If $x$ is divisible by $4$ then $x$ is not divisible by $2$
Answer
Correct option: A.
If $x$ is divisible by $2$ then $x$ must be divisible by $4$
Converse statement for given statement $“$if $p$ then $q”$ is $“$if $q$ then $p”$
i.e. $q \Rightarrow p.$
So, converse for $“$If $x$ is divisible by $4$ then $x$ must be divisible by $2”$ is $“$If $x$ is divisible by $2$ then $x$ is must be divisible by $4”.$
View full question & answer→
MCQ 501 Mark
If $p \rightarrow (p ∧ \sim q)$ is false, then the truth values of $p$ and $q$ are respectively\sim .
  • A
    $F, F$
  • B
    $T, F$
  • ✓
    $T, T$
  • D
    $F, T$
Answer
Correct option: C.
$T, T$
View full question & answer→
MCQ 511 Mark
Choose the correct answer:
The converse of the statement.
$“$If $x > y,$ then $x + a > y + a”$ is.
  • A
    If $x < y,$ then $x + a < y + a$.
  • ✓
    If $x + a > y + a,$ then $x > y.$
  • C
    If $x < y,$ then $x + a > y + a.$
  • D
    If $x > y,$ then $x + a < y + a.$
Answer
Correct option: B.
If $x + a > y + a,$ then $x > y.$
Let $p: x > y$
$q: x + a > y + a$
$P \Rightarrow q$
Converse of the above statement is:
$q \Rightarrow P$
i.e., If $x + a > y + a,$ then $x > y$
View full question & answer→
MCQ 521 Mark
What is converse for statement if $p$ then $q\ ?$
  • A
    If not $q$ then not $p$
  • ✓
    If $q$ then $p$
  • C
    If not $p$ then $q$
  • D
    If not $p$ then not $q$
Answer
Correct option: B.
If $q$ then $p$
Converse statement for given statement $“$if $p$ then $q”$ is $“$if $q$ then $p”$
i.e. $q \Rightarrow p$ or $q$ implies $p.$
View full question & answer→
MCQ 531 Mark
The method $(s)$ that are used to check the validity of statements is:
  • A
    contrapositive method
  • B
    method of contradiction
  • C
    using a counter example
  • ✓
    All the above
Answer
Correct option: D.
All the above
The methods that are used to check the validity of statements include the following.
direct method
contrapositive method
method of contradiction
using a counter example
View full question & answer→
MCQ 541 Mark
The negation of the statement $(p\ Λ\ q) \rightarrow (\sim p ∨ r)$ is.
  • A
    $(p\ Λ\ q) ∨ (p\ ∨ \sim r)$
  • B
    $(p\ Λ\ q) ∨ (p\ Λ \sim r)$
  • ✓
    $(p\ Λ\ q)\ Λ\ (p\ Λ \sim r)$
  • D
    $p ∨ q$
Answer
Correct option: C.
$(p\ Λ\ q)\ Λ\ (p\ Λ \sim r)$
View full question & answer→
MCQ 551 Mark
If $p$ then $q$ means $............$ is sufficient condition for $............$
  • A
    $p, p$
  • B
    $q, q$
  • ✓
    $p, q$
  • D
    $q, p$
Answer
Correct option: C.
$p, q$
If $p$ then $q$ means $p$ is sufficient condition for $q$ or $p \Rightarrow q.$
It is not same as $q$ is sufficient condition for $p.$
View full question & answer→
MCQ 561 Mark
Which of the following is a statement.
  • A
    $x$ is a real number
  • B
    Switch of the fan
  • ✓
    $6$ is a natural number
  • D
    Let me go
Answer
Correct option: C.
$6$ is a natural number
The statement $6$ is a natural number is true.
So, it is a statement.
View full question & answer→
MCQ 571 Mark
Kiran passed the examination, $q:$ Kiran is sad.
The symbolic form of a statement "It is not true that Kiran passed therfore he is said'' is.
  • A
    $(\sim p \rightarrow q)$
  • ✓
    $(p \rightarrow q)$
  • C
    $\sim (p \rightarrow \sim q)$
  • D
    $\sim ( p \rightarrow q)$
Answer
Correct option: B.
$(p \rightarrow q)$
View full question & answer→
MCQ 581 Mark
The negation of the proposition ''if a quadrilateral is a square, then it is a rhombus'' is.
  • A
    If a quadrilateral is not a square, then it is a rhombus.
  • B
    A quadrilateral is not a square and it is a rhombus.
  • C
    If a quadrilateral is a square, then it is not a rhombus.
  • ✓
    A quadrilateral is a square and it is not a rhombus.
Answer
Correct option: D.
A quadrilateral is a square and it is not a rhombus.
View full question & answer→
MCQ 591 Mark
If $p \Rightarrow (q ∨ r)$ is false, then the truth values of $p, q, r$ are respectively.
  • ✓
    $\text{T, F, F}$
  • B
    $\text{F, F, F}$
  • C
    $\text{F, T, T}$
  • D
    $\text{T, T, F}$
Answer
Correct option: A.
$\text{T, F, F}$
View full question & answer→
MCQ 601 Mark
The negation of the statement The product of $3$ and $4$ is $9$ is.
  • ✓
    It is false that the product of $3$ and $4$ is $9$
  • B
    The product of $3$ and $4$ is $12$
  • C
    The product of $3$ and $4$ is not $12$
  • D
    It is false that the product of $3$ and $4$ is not $9$
Answer
Correct option: A.
It is false that the product of $3$ and $4$ is $9$
Given, statement is The product of $3$ and $4$ is $9$
The negation of the statement is:
It is false that the product of $3$ and $4$ is $9$
View full question & answer→
MCQ 611 Mark
Choose the correct answer:
The contrapositive of statement ‘If Chandigarh is capital of Punjab, then Chandigarh is in India’ is.
  • ✓
    If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.
  • B
    If Chandigarh is in India, then Chandigarh is Capital of Punjab.
  • C
    If Chandigarh is not capital of Punjab, then Chandigarh is not capital of India.
  • D
    If Chandigarh is capital of Punjab, then Chandigarh is not in India.
Answer
Correct option: A.
If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.
Let $p:$ Chandigarh is capital of Punjab.
and $q:$ Chandigarh is in India.
$\sim p:$ Chandigarh is not capital of Punjab.
$\sim q:$ Chandigarh is not in India.
Contra positive of the statement $p \rightarrow q$
if $(\sim q)$, then $(\sim p).$
It Chandigarh is not in India, then Chandigarh is not the capital of Punjab.
View full question & answer→
MCQ 621 Mark
Which of the following is not a statement?
  • A
    Product of $1$ and $2$ is $-4.$
  • B
    Squares are always positive.
  • ✓
    Give me a cup of tea.
  • D
    Sum of $2$ and $3$ is $9$.
Answer
Correct option: C.
Give me a cup of tea.
Give me a cup of tea.
View full question & answer→
MCQ 631 Mark
The proposition $(p \rightarrow \sim p) ∧ (\sim p \rightarrow p)$ is
  • ✓
    a contradiction
  • B
    a contradiction and a tautology
  • C
    neither a contradiction nor a tautolog
  • D
    a tautology
Answer
Correct option: A.
a contradiction
View full question & answer→
MCQ 641 Mark
Which of the following is converse of “If $x$ is divisible by $4$ then $x$ must be divisible by $2”\ ?$
  • ✓
    If $x$ is divisible by $2$ then $x$ must be divisible by $4$
  • B
    If $x$ is not divisible by $2$ then $x$ must be divisible by $4$
  • C
    If $x$ is not divisible by $2$ then $x$ is not divisible by $4$
  • D
    If $x$ is divisible by $4$ then $x$ is not divisible by $2$
Answer
Correct option: A.
If $x$ is divisible by $2$ then $x$ must be divisible by $4$
Converse statement for given statement “if $p$ then $q”$ is “if $q$ then $p”$ i.e. $q ⇒ p.$
So, converse for “If $x$ is divisible by $4$ then $x$ must be divisible by $2”$ is “If $x$ is divisible by $2$ then $x$ is must be divisible by $4”.$
View full question & answer→
MCQ 651 Mark
Sentence involving variable time such as today, tomorrow, or yesterday are.
  • A
    Statements
  • ✓
    Not statements
  • C
    May or may not be statements
  • D
    None of these
Answer
Correct option: B.
Not statements
Sentence involving variable time such as today, tomorrow, or yesterday are not statements.
This is because it is not known what time is referred here.
View full question & answer→
MCQ 661 Mark
If $x = 5$ and $y = - 2,$ then $x - 2y = 9.$ The contrapositive of this proposition is.
  • A
    $x - 2y = 9$ if $x = 5$ and $y = - 2$
  • B
    If $x - 2y = 9, x ≠ 5$ and $y ≠ - 2$
  • ✓
    If $x - 2y = 9,$ then $x ≠ 5$ or $y ≠ - 2$
  • D
    None of these
Answer
Correct option: C.
If $x - 2y = 9,$ then $x ≠ 5$ or $y ≠ - 2$
View full question & answer→
MCQ 671 Mark
Which of the following statements is logically equivalent to "The solution is easy if you read the question carefully."?
  • ✓
    If you do not read the question carefully, the solution is hard.
  • B
    If the solution is easy, then you read the question carefully.
  • C
    If the solution is hard, then you did not read the question carefully.
  • D
    None of these.
Answer
Correct option: A.
If you do not read the question carefully, the solution is hard.
Given Statement:
The solution is easy if you read the question carefully.
Logically equivalent statement:
If you do not read the question carefully, the solution is hard.
View full question & answer→
MCQ 681 Mark
Connect $“0$ is positive number” and $“0$ is a negative number”?
  • ✓
    $0$ is a positive or negative number
  • B
    $0$ is a positive and negative number
  • C
    $0$ is either positive or negative number
  • D
    $0$ is neither positive nor negative number
Answer
Correct option: A.
$0$ is a positive or negative number
$“0$ is a positive or negative number” is formed by connecting the given statements using or.
View full question & answer→
MCQ 691 Mark
Choose the correct answer : The negation of the statement.
“A circle is an ellipse” is.
  • A
    An ellipse is a circle.
  • B
    An ellipse is not a circle.
  • ✓
    A circle is not an ellipse.
  • D
    A circle is an ellipse.
Answer
Correct option: C.
A circle is not an ellipse.
Let $p:$ A circle is an ellipse.
$\sim p:$ A circle is not an ellipse.
View full question & answer→
MCQ 701 Mark
Negation of the statement "Every natural number is an integer".
  • A
    All natural numbers are whole numbers.
  • B
    Every natural number is not a real number.
  • ✓
    Every natural number is not an integer.
  • D
    none of the above.
Answer
Correct option: C.
Every natural number is not an integer.
Negation of "Every Natural number is an integer". is "Every Natural number is $\text{NOT}$ an integer".
View full question & answer→
MCQ 711 Mark
Which of the following is a statement?
  • A
    There are $27$ days in this month
  • B
    February has $28$ days
  • C
    February has $29$ days
  • ✓
    There are $32$ days in this month
Answer
Correct option: D.
There are $32$ days in this month
When we talk about this, that, here, there, we are not sure about what we are talking about so “There are $27$ days in this month” is not a statement.
“February has $28$ days” and “February has $29$ days” both are not statements because February may have $28$ days or $29$ das based on the year. “There are $32$ days in this month” is a statement as it is false.
We cannot have $32$ days in a month.
View full question & answer→
MCQ 721 Mark
Choose the correct answer: The contrapositive of the statement.
“If $p,$ then $q”,$ is.
  • A
    If $q,$ then $p.$
  • B
    If $p,$ then $\sim q.$
  • ✓
    If $\sim q$, then $\sim p.$
  • D
    If $\sim p,$ then $\sim q.$
Answer
Correct option: C.
If $\sim q$, then $\sim p.$
$p \rightarrow q$
If $p,$ then $q$
Contra positive of the statement $p \rightarrow q$ is $(\sim q) \rightarrow (\sim p).$
If $\sim q,$ then $\sim p.$
View full question & answer→
MCQ 731 Mark
Choose the correct answer:
The connective in the statement.
“Earth revolves round the Sun and Moon is a satellite of earth” is.
  • A
    or.
  • B
    Earth.
  • C
    Sun.
  • ✓
    and.
Answer
Correct option: D.
and.
Connective word is “and”.
View full question & answer→
MCQ 741 Mark
Which of the following is not a negation of the statement A natural number is greater than zero.
  • A
    A natural number is not greater than zero
  • B
    It is false that a natural number is greater than zero
  • ✓
    It is false that a natural number is not greater than zero
  • D
    None of these
Answer
Correct option: C.
It is false that a natural number is not greater than zero
Given statement is:
A natural number is greater than zero
View full question & answer→
MCQ 751 Mark
The contrapositive of $(\sim p ∧ q) \rightarrow$ is.
  • A
    $(p ∨ q) \rightarrow r$
  • ✓
    $r \rightarrow (p\ ∨ \sim q)$
  • C
    $(p ∧ q) \rightarrow r$
  • D
    None of these
Answer
Correct option: B.
$r \rightarrow (p\ ∨ \sim q)$
View full question & answer→
MCQ 761 Mark
If $(p ∧ ~r) \Rightarrow (q ∨ r)$ is false and $q$ and $r$ are both false, then $p$ is.
  • ✓
    True
  • B
    False
  • C
    May be true or false
  • D
    Data sufficient Answer
Answer
Correct option: A.
True
View full question & answer→
MCQ 771 Mark
Which of the following pairs is logically equivalent?
  • A
    Contrapositive, Converse
  • B
    Conditional, Inverse
  • C
    Inverse, Contrapositive
  • ✓
    Conditional, Contrapositive
Answer
Correct option: D.
Conditional, Contrapositive
View full question & answer→
MCQ 781 Mark
If $p$ then $q$ means $............$ is sufficient condition for $............$
  • A
    $p, p$
  • B
    $q, q$
  • ✓
    $p, q$
  • D
    $q, p$
Answer
Correct option: C.
$p, q$
If $p$ then $q$ means $p$ is sufficient condition for $q$ or $p \Rightarrow q.$
It is not same as $q$ is sufficient condition for $p.$
View full question & answer→
MCQ 791 Mark
Let $p$ and $q$ be two prepositions given by
$p :$ I play cricket during the holidays,
$q :$ I just sleep throughout the day then, the compound statement $p ∧ q$ is.
  • ✓
    I play cricket during the holidays and just sleep throughout the day.
  • B
    If I play cricket during the holidays, I just sleep throughout the day.
  • C
    I play cricket during the holidays or just sleep throughout the day.
  • D
    I just sleep throughout the day if and only if I play cricket during the holidays.
Answer
Correct option: A.
I play cricket during the holidays and just sleep throughout the day.
View full question & answer→
MCQ 801 Mark
Which of the following is not a statement?
  • A
    Two and two makes four
  • B
    A prime number is always odd
  • ✓
    Sum of $a$ and $b$ is $5$
  • D
    Elephant is heavier than ant
Answer
Correct option: C.
Sum of $a$ and $b$ is $5$
“Two and two makes four” and “Elephant is heavier than ant” are true so they are statements. “A prime number is always odd” is false as prime number may be even so it is a statement. “Sum of and b is $5”$ is not a statement as it can be true or false based on the values of $a$ and $b$ taken.
View full question & answer→
MCQ 811 Mark
The negation of $(p ∨ q)\ Λ\ (p\ ∨ \sim r)$ is.
  • A
    $(\sim p\ Λ \sim q) ∨ (q\ Λ \sim r)$
  • B
    $(\sim p\ Λ \sim q) ∨ (\sim q\ Λ\  r)$
  • ✓
    $(\sim p\ Λ \sim q) ∨ (\sim q\ Λ\ r)$
  • D
    $(\sim p\ Λ\ \sim q) ∨ (q\ Λ \sim r)$
Answer
Correct option: C.
$(\sim p\ Λ \sim q) ∨ (\sim q\ Λ\ r)$
View full question & answer→
MCQ 821 Mark
The contrapositive of the statement "If you believe in yourself and are honest then you will get sucess" is:
  • A
    If you do not believe yourself and are dishonest then you will not get success.
  • B
    If you do not believe yourself and are dishonest then you will get success.
  • C
    If you get success then you are honest and you also believe in yourself.
  • ✓
    If you will not get success then you don't not believe in yourself or are not honest.
Answer
Correct option: D.
If you will not get success then you don't not believe in yourself or are not honest.
Sometimes in mathematics, it's important to determine what the opposite of a given mathematical statement is. This is usually referred to as "negating" a statement.
One thing to keep in mind is that if a statement is true, then its negation is false $($and if a statement is false, then its negation is true$).$
So, If (something is done), then $($something happens$),$
Negation: If $($something is done$),$ then $($something does not happen$),$
you believe in yourself and are honest and did not get success.
View full question & answer→
MCQ 831 Mark
In the truth table for the statement $( \sim p \rightarrow \sim q)\ ∧\ (\sim q \rightarrow \sim p),$ the last column has the truth value in the following order is.
  • A
    $\text{T, T, T, F}$
  • B
    $\text{F, T, T, F}$
  • ✓
    $\text{T, F, F, T}$
  • D
    $\text{T, T, T, T}$
Answer
Correct option: C.
$\text{T, F, F, T}$
View full question & answer→
MCQ 841 Mark
A sentence is called statement if it is $...............$
  • A
    Always true
  • B
    Always false
  • ✓
    Either true or false but not both
  • D
    Both true and false
Answer
Correct option: C.
Either true or false but not both
A sentence is called mathematically acceptable statement if it is either true or false but not both.
View full question & answer→
MCQ 851 Mark
Choose the correct answer:
The connective in the statement.
$“2 + 7 > 9$ or $2 + 7 < 9”$ is
  • A
    and
  • ✓
    or
  • C
    $ > $
  • D
    $ < $
Answer
Correct option: B.
or
In $‘2 + 7 > 9$ or $2 + 7 < 9’$ the connective is ‘or’.
View full question & answer→
MCQ 861 Mark
If $p$ then $q$ means $............$
  • A
    If $q$ then $p$
  • ✓
    $p \Rightarrow q$
  • C
    $q \Rightarrow p$
  • D
    $q$ only if $p$
Answer
Correct option: B.
$p \Rightarrow q$
If $p$ then $q$ means $p$ implies $q$ i.e. $p \Rightarrow q.$
This does not mean $q \Rightarrow p.$
$Q$ only if $p$ means $q \Rightarrow p.$
View full question & answer→
MCQ 871 Mark
The negative of the statement "If a number is divisible by $15$ then it is divisible by $5$ or $3":$
  • A
    If a number is not divisible by $15,$ then it is not divisible by $5$ and $3.$
  • B
    A number is divisible by $15$ and it is not divisible by $5$ or $3.$
  • C
    A number is not divisible by $15$ or it is not divisible by $5$ and $3.$
  • ✓
    A number is divisible by $15$ and it is not divisible by $5$ and $3.$
Answer
Correct option: D.
A number is divisible by $15$ and it is not divisible by $5$ and $3.$
Let $p, q, r$ be three statements defined as
$p :$ a number $N$ is divisible by $15$
$q :$ number $N$ is divisible by $5$
$r :$ number $N$ is divisible by $3$
Here given statement is $p \rightarrow (q∨r)$
Here negative of above statement is
$\sim (p \rightarrow (q∨r)) ≡ p ∧ ( \sim (q∨r)$
$≡ p ∧ (\sim q∧\sim r)$
i.e. A number is divisible by $15$ and it is not divisible by $5$ and $3.$
View full question & answer→
MCQ 881 Mark
Which of the following is not a statement:
  • A
    The product of $(-1)$ and $8$ is $8$
  • B
    All complex number are real number
  • C
    Today is windy day
  • ✓
    All of the above
Answer
Correct option: D.
All of the above
A sentence is a statement if it is true.
None of the above sentence is true.
View full question & answer→
MCQ 891 Mark
"If Deb and Sam go to the mall then it is snowing"
Which statement below is logically equivalent?
  • A
    If Deb and Sam do not go to the mall then it is not snowing.
  • B
    If Deb and Sam do not go to the mall them it is snowing.
  • C
    If it is snowing then Deb and Sam go to the mall.
  • ✓
    If it is not snowing then Deb and Sam do not go to the mall.
Answer
Correct option: D.
If it is not snowing then Deb and Sam do not go to the mall.
Deb and Sam go to the mall only if it is snowing which means if it is not snowing, they don't go to the mall.
View full question & answer→
MCQ 901 Mark
The contrapositive of $2x + 3 = 9 \Rightarrow x \neq 4$ is.
  • A
    $x \neq 4, 2x + 3 \neq 9$
  • ✓
    $x = 4, 2x + 3 \neq 9$
  • C
    $x = 4, 2x + 3 = 9$
  • D
    $x \neq 4, 2x + 3 = 9$
Answer
Correct option: B.
$x = 4, 2x + 3 \neq 9$
View full question & answer→
MCQ 911 Mark
Which one of the following statements is not a false statement?
  • A
    $p:$ Each radius of a circle is a chord of the circle.
  • ✓
    $q:$ Circle is a particular case of an ellipse.
  • C
    $r:​ \sqrt3$ is a rational number.
  • D
    $s:$ The centre of a circle bisects each chord of the cirlce.
Answer
Correct option: B.
$q:$ Circle is a particular case of an ellipse.
We know that equation of an ellipse is given by $\frac{\text{x}^2}{\text{a}^2}+\frac{\text{y}^2}{\text{b}^2}=1$
If we take $a = b$ then we get $x^2 + y^2 = a^2$ which satisfies all the conditions of circle
$\therefore$ circle is the particular case of an ellipse.
View full question & answer→
MCQ 921 Mark
The converse of the statement “If $x > y,$ then $x + a > y + a”$ is
  • A
    If $x < y,$ then $x + a < y + a.$
  • ✓
    If $x + a > y + a,$ then $x > y.$
  • C
    If $x < y,$ then $x + a > y + a.$
  • D
    If $x > y,$ then $x + a < y + a.$
Answer
Correct option: B.
If $x + a > y + a,$ then $x > y.$
As we know, the converse of a statement $p \Rightarrow q$ is the statement $q \Rightarrow p.$
So, the converse of the statement “If $x > y,$ then $x + a > y + a”$ is.
If $x + a > y + a,$ then $x > y.$
View full question & answer→
MCQ 931 Mark
Choose the correct answer:
Which of the following is not a negation of “A natural number is greater than zero”.
  • A
    A natural number is not greater than zero.
  • B
    It is false that a natural number is greater than zero.
  • ✓
    It is false that a natural number is not greater than zero.
  • D
    None of the above.
Answer
Correct option: C.
It is false that a natural number is not greater than zero.
The negation of the given statement is false. i.e., It is false that a natural number is not greater than zero.
View full question & answer→
MCQ 941 Mark
The converse of "If $x$ has courage, then $x$ will win", is:
  • ✓
    If $x$ wins, then $x$ has courage.
  • B
    If $x$ has no courage, then $x$ will not win.
  • C
    If $x$ will not win, then $x$ has no courage.
  • D
    If $x$ will not win, then $x$ has courage.
Answer
Correct option: A.
If $x$ wins, then $x$ has courage.
Take $p : x$ has courage
and $q : x$ will win
So the given conjugation is $p \Rightarrow q$
Now we need to find converse of this.
Be definition, Converse will be $q \Rightarrow p$
This is symbolic for "If $x$ wins then $x$ has courage
View full question & answer→
MCQ 951 Mark
The negation of the statement “Akash or Ankitha lived in Goa” is:
  • A
    Akash did not live in Goa or Ankitha lives in Goa.
  • B
    Akash lives in Goa and Ankitha did not live in Goa.
  • ✓
    Akash did not live in Goa and Ankitha did not live in Goa.
  • D
    Akash did not live in Goa or Ankitha did not live in Goa.
Answer
Correct option: C.
Akash did not live in Goa and Ankitha did not live in Goa.
Given,
Statement: Akash or Ankitha lived in Goa
Negation of the above statement is:
Akash did not live in Goa and Ankitha did not live in Goa.
View full question & answer→
MCQ 961 Mark
Which of the following is not a statement?
  • A
    Smoking is injurious to health.
  • B
    $2 + 2 = 4$
  • C
    $2$ is the only even prime number.
  • ✓
    Come here.
Answer
Correct option: D.
Come here.
Smoking is injurious to health.
It is a statement.
$2 + 2 = 4;$ It is a mathematical statement.
$2$ is the only even prime number.
Mathematical statement.
Come here.
It is not a statement but it is an order.
View full question & answer→
MCQ 971 Mark
The contrapositive of the statement ‘If Chandigarh is the capital of Punjab, then Chandigarh is in India’ is
  • ✓
    If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.
  • B
    If Chandigarh is in India, then Chandigarh is the capital of Punjab.
  • C
    If Chandigarh is not the capital of Punjab, then Chandigarh is not the capital of India.
  • D
    If Chandigarh is the capital of Punjab, then Chandigarh is not in India.
Answer
Correct option: A.
If Chandigarh is not in India, then Chandigarh is not the capital of Punjab.
View full question & answer→
MCQ 981 Mark
The propositions $(p \Rightarrow \sim p)\ Λ\ \sim p \Rightarrow p)$ is.
  • A
    Tautology and contradiction
  • B
    Neither tautology nor contradiction
  • ✓
    Contradiction
  • D
    Tautology
Answer
Correct option: C.
Contradiction
View full question & answer→
MCQ 991 Mark
In the truth table for the statement $\sim ( \sim p ∨ \sim q),$ the last column has the truth value in the following order.
  • ✓
    $\text{TFFF}$
  • B
    $\text{TTFT}$
  • C
    $\text{FTTF}$
  • D
    $\text{FFFT}$
Answer
Correct option: A.
$\text{TFFF}$
View full question & answer→
MCQ 1001 Mark
Which of the following statement is true?
  • A
    $25$ is divisible by $2$ and $3$
  • B
    $12$ is a positive and prime number
  • ✓
    $13$ is a positive and odd number
  • D
    $49$ is a square and a cube
Answer
Correct option: C.
$13$ is a positive and odd number
For a statement with ‘and’, if both statements are true then the given statement will be true.
In statement $“25$ is divisible by $2$ and $3”, 25$ is divisible by $2$ is true but $25$ is divisible by $3$ is false so it is false statement.
In statement $“12$ is a positive and prime number”, $12$ is a positive number is true but $12$ is a prime number is false so it is a false statement.
In statement $“13$ is a positive and odd number”, both statements i.e. $13$ is a positive number and $13$ is an odd number are true so it is a true statement.
In statement $“49$ is a square and a cube”, $49$ is a square is true but $49$ is a cube is false so it is a false statement.
View full question & answer→
MCQ 1011 Mark
The inverse of the statement "If a person is mean, then they are a fighter" is:
  • A
    If a person is not mean, then they are a fighter.
  • B
    If a person is mean, then they are not a fighter.
  • ✓
    If a person is not mean, then they are not a fighter.
  • D
    None of the above.
Answer
Correct option: C.
If a person is not mean, then they are not a fighter.
A person is not mean is the negation of the hypothesis that a person is mean and they are not a fighter is the negation of the conclusion they are a fighter.
View full question & answer→
MCQ 1021 Mark
Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”
  • A
    If a number is not a prime then it is prime
  • ✓
    If a number is not a prime then it is odd
  • C
    If a number is not odd then it is not a prime
  • D
    If a number is not odd then it is a prime
Answer
Correct option: B.
If a number is not a prime then it is odd
View full question & answer→
MCQ 1031 Mark
Which of the following compound statement has both true component statements?
  • A
    A prime number is divisible by $2$ and odd
  • B
    Two and two makes four or five
  • C
    All integers are positive and divisible by $2$
  • ✓
    $100$ is divisible by $2$ and $5$
Answer
Correct option: D.
$100$ is divisible by $2$ and $5$
Prime number is not divisible by $2$ always.
Two and two makes our not five.
All integers are not positive.
$100$ is divisible by $2$ and $5$ both.
So, component statements of $“100$ is divisible by $2$ and $5”$ are true.
View full question & answer→
MCQ 1041 Mark
Mary says "The number I am thinking is divisible by $2$ or it is divisible by $3"$. This statement is false if the number Mary is thinking of is:
  • A
    $6$
  • B
    $8$
  • ✓
    $11$
  • D
    $15$
Answer
Correct option: C.
$11$
The statement is true if Mary is thinking of:
As, $6$ is divisible by both $2$ and $3.$
As, $8$ is divisible by $2.$
As, $15$ is divisible by $3.$
Hence, the statement is false for option $(C)$ as $11$ is not divisble by either $2$ or $3.$
View full question & answer→
MCQ 1051 Mark
What is contrapositive for statement if $p$ then $q\ ?$
  • ✓
    If not $q$ then not $p$
  • B
    If $q$ then $p$
  • C
    If not $p$ then $q$
  • D
    If not $p$ then not $q$
Answer
Correct option: A.
If not $q$ then not $p$
Contrapositive statement for given statement “if $p$ then $q”$ is “if not $q$ then not $p”$
i.e. $\sim q \Rightarrow \sim p.$
View full question & answer→
MCQ 1061 Mark
If $\text{p, q, r}$ are statement with truth vales $\text{F, T, F}$ respectively then the truth value of $p \rightarrow (q \rightarrow r)$ is.
  • A
    false
  • ✓
    true
  • C
    true if $p$ is true
  • D
    none
Answer
Correct option: B.
true
View full question & answer→
MCQ 1071 Mark
“If $p$ then $q”$ is true when $.............$
  • A
    $p \Rightarrow q$
  • B
    $q \Rightarrow p$
  • C
    $p \Rightarrow$ not $q$
  • ✓
    both $p \Rightarrow q$ and $q \Rightarrow p$
Answer
Correct option: D.
both $p \Rightarrow q$ and $q \Rightarrow p$
If $p$ then $q$ statement will be true.
If $p$ is true then $q$ must be true and if $q$ is true then $p$ must be true.
View full question & answer→
MCQ 1081 Mark
Which of the following statements is the inverse of "If you do not understand geometry, then you do not know how to reason deductively."?
  • ✓
    If you reason deductively, then you understand geometry.
  • B
    If you understand geometry, then you reason deductively.
  • C
    If the do not reason deductively, then you understand geometry.
  • D
    None of these
Answer
Correct option: A.
If you reason deductively, then you understand geometry.
To find the inverse we need to negate the hypothesis and conclusion. On negating the hypothesis we get you reason deductively and on negating the conclusion we get you understand geometry.
View full question & answer→
MCQ 1091 Mark
Which of the following is a statement?
  • A
    Women are more intelligent than men
  • ✓
    Two plus two is three
  • C
    Open the door
  • D
    Shut your mouth
Answer
Correct option: B.
Two plus two is three
A sentence is called mathematically acceptable statement if it is either true or false but not both
“Two plus ''two is three” is false so it is a statement.
Rest we cannot decide whether they are true or false.
View full question & answer→
MCQ 1101 Mark
In contrapositive method to prove statement “If $p$ then $q”$ is valid or not, we assume $p$ to be $..........$ and prove $q$ to be $..........$
  • A
    true, false
  • B
    true, true
  • ✓
    false, false
  • D
    false, true
Answer
Correct option: C.
false, false
In contrapositive method, we assume $p$ to be false and use it to prove that $q$ is also false.
There is no case for $p$ to be true in direct method.
View full question & answer→
MCQ 1111 Mark
If $p$ then $q$ means $..........$ implies $..........$
  • A
    $q \Rightarrow p$
  • ✓
    $\sim q \Rightarrow \sim p$
  • C
    $\sim p \Rightarrow \sim q$
  • D
    $p \Rightarrow \sim q$
Answer
Correct option: B.
$\sim q \Rightarrow \sim p$
If $p$ then $q$ means $p \Rightarrow q$ or negation of $q$ implies negation of $p$
i.e. $\sim q \Rightarrow \sim p.$
View full question & answer→
MCQ 1121 Mark
An analysis of the monthly wages paid to the workers of a form is given below. Calculate the total monthly wages.
No. of workers
 $100$
Average monthly wages
 $280$
Variance of distribution of wages
 $10$
 
  • A
    $2800$
  • B
    $280$
  • ✓
    $28000$
  • D
    $2.8$
Answer
Correct option: C.
$28000$
Number of wage earners $(n_1) = 100$
Mean of monthly wages $(X_1) = ₹ 280$
Mean of monthly wages $=$ Total monthly wage/ Number of workers
$\Rightarrow 280 =\frac{\text{total monthly wages}}{100}$
$\Rightarrow \text{Total monthly}= \frac{\text{wages}} {28000}.$
View full question & answer→
MCQ 1131 Mark
Choose the correct answer: Which of the following is not a statement.
  • A
    Smoking is injurious to health.
  • B
    $2 + 2 = 4.$
  • C
    $2$ is the only even prime number.
  • ✓
    Come here.
Answer
Correct option: D.
Come here.
To given order cannot be a statement.
So ‘Come here’ is not a statement.
View full question & answer→
MCQ 1141 Mark
If $p$ then $q$ means $..........$ is necessary condition for $..........$
  • A
    $p, p$
  • B
    $q, q$
  • C
    $p, q$
  • ✓
    $q, p$
Answer
Correct option: D.
$q, p$
If $p$ then $q$ means $q$ is necessary condition for $p$ or $p \Rightarrow q.$
It is not same as $p$ is necessary condition for $q.$
View full question & answer→
MCQ 1151 Mark
The negation of the Boolean expression $\sim s ∨ (\sim r ∧ s)$ is equivalent to:
  • A
    $\sim s\ ∧ \sim r$
  • B
    $r$
  • C
    $s ∨ r$
  • ✓
    $s ∧ r$
Answer
Correct option: D.
$s ∧ r$
View full question & answer→
MCQ 1161 Mark
The inverse of "If $x$ has courage, then $x$ will win", is:
  • A
    If $x$ will win, then $x$ has courage.
  • ✓
    If $x$ has no courage, then $x$ will not win.
  • C
    If $x$ will not win, then $x$ has no courage.
  • D
    If $x$ will not win, then $x$ has courage.
Answer
Correct option: B.
If $x$ has no courage, then $x$ will not win.
Take $p : x$ has courage
And $q : x$ will win
So the given conjugation is $p \Rightarrow q$
Now we need to find Inverse of this.
Be definition, Inverse of $p \Rightarrow q$ is $\sim p ⟶ \sim q$
$\sim p : x$ has no courage,
$\sim q : x$ will not win
Thus the inverse $\sim p ⟶ \sim q$ is symbolic form of "If $x$ has no courage, then $x$ will not win.
View full question & answer→
MCQ 1171 Mark
Choose the conclusion of given statements:
All scientists working in America are talented. Some Indian scientists are working in America. Therefore, "Some Indian scientists are talented."
  • ✓
    True
  • B
    May be true
  • C
    False
  • D
    May be false
Answer
Correct option: A.
True
The statement is true as it's already given that All scientists working in America are talented.
View full question & answer→
MCQ 1181 Mark
Which of the following is a statement?
  • A
    Close the door
  • ✓
    $11$ comes after $12$
  • C
    India is a beautiful country
  • D
    This is useless
Answer
Correct option: B.
$11$ comes after $12$
“Close the door” is not a statement as it is an imperative sentence.
$“11$ comes after $12”$ is a statement as it is true.
“India is a beautiful country” is not a statement as opinion of beautifulness vary from person to person.
“This is useless” is not a statement as it involves this which doesn’t give any idea about what we are talking.
View full question & answer→
MCQ 1191 Mark
$R$ the following statements.
$P:$ Suman is brilliant
$Q:$ Suman is rich
$R:$ Suman is honest
The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as.
  • ✓
    $\sim (Q \rightarrow (P\ Λ \sim R))$
  • B
    $\sim Q \rightarrow ~P\ Λ\ R$
  • C
    $\sim P\ Λ\ \sim R) \rightarrow Q$
  • D
    $\sim P\ Λ\ (Q \rightarrow \sim R)$
Answer
Correct option: A.
$\sim (Q \rightarrow (P\ Λ \sim R))$
View full question & answer→
MCQ 1201 Mark
Choose the correct answer:
The negation of the statement.
$“7$ is greater than $8”$ is.
  • A
    $7$ is equal to $8.$
  • ✓
    $7$ is not greater than $8.$
  • C
    $8$ is less than $7.$
  • D
    none of these.
Answer
Correct option: B.
$7$ is not greater than $8.$
Let $p: 7$ is greater than $8.$
$\sim p: 7$ is not greater than $8.$
View full question & answer→
MCQ 1211 Mark
The negation of the statement $7$ is greater than $8$ is:
  • A
    $7$ is equal to $8.$
  • ✓
    $7$ is not greater than $8.$
  • C
    $8$ is less than $7.$
  • D
    none of these.
Answer
Correct option: B.
$7$ is not greater than $8.$
Statement: $7$ is greater than $8$
Negation: $7$ is not greater than $8$
View full question & answer→
MCQ 1221 Mark
The converse of the statement $p \Rightarrow q$ is.
  • A
    $p \Rightarrow q$
  • ✓
    $q \Rightarrow p$
  • C
    $~p \Rightarrow q$
  • D
    $~q \Rightarrow p$
Answer
Correct option: B.
$q \Rightarrow p$
The converse of the statement $p \Rightarrow q$ is
$q \Rightarrow p$
View full question & answer→
MCQ 1231 Mark
Choose the correct answer:
The negation of the statement.
“Plants take in $CO_2$ and give out $O_2$ ” is.
  • A
    Plants do not take in $CO_2$ and do not give out $O_2$
  • ✓
    Plants do not take in $CO_2$ or do not give out $O_2$.
  • C
    Plants take in $CO_2$ and do not give out $O_2$
  • D
    Plants take in $CO_2$ or do not give out $O_2$.
Answer
Correct option: B.
Plants do not take in $CO_2$ or do not give out $O_2$.
Let $p:$ Plants take in $CO_2$ and give out $O_2$
$q:$ Plants take in $CO_2$
$r:$ Plants give out $O_2$
$\sim q:$ Plants do not take in $CO_2$.
$\sim r:$ Plants do not give out$O_2$.
$\therefore\ \sim (q ^ r) = (\sim q \sim r):$ plants do not take in $CO_2$​​​​​​​ or do not give out $O_2$
View full question & answer→
MCQ 1241 Mark
The contra$-$positive of the statement If a triangle is not equilateral, it is not isosceles is:
  • A
    If a triangle is not equilateral, it is not isosceles
  • B
    If a triangle is equilateral, it is not isosceles
  • C
    If a triangle is not equilateral, it is isosceles
  • ✓
    If a triangle is equilateral, it is isosceles
Answer
Correct option: D.
If a triangle is equilateral, it is isosceles
Given, statement is:
If a triangle is not equilateral, it is not isosceles.
Now, contra$-$positive is:
If a triangle is equilateral, it is isosceles.
View full question & answer→
MCQ 1251 Mark
Which of the following is true.
  • A
    A prime number is either even or odd
  • B
    $\sqrt{3}$ is irrational number.
  • C
    $24$ is a multiple of $2, 4$ and $8$
  • ✓
    Everyone in India speaks Hindi.
Answer
Correct option: D.
Everyone in India speaks Hindi.
The statement Everyone in India speaks Hindi is not true.
This is because, there are some states like Tamil nadu, Kerala, etc.
where the person does not speak Hindi.
View full question & answer→
MCQ 1261 Mark
Earth is a planet. Choose the option that is a negation of this statement:
  • A
    Earth is round
  • B
    Earth is not round
  • C
    Earth revolves round the sun
  • ✓
    Earth is not a planet
Answer
Correct option: D.
Earth is not a planet
Negation of statement $"P"$ is $"$not $P"$
View full question & answer→
MCQ 1271 Mark
$f$ the Boolean expression $(p ⊕ q) ∧ (\sim p ⊗ q)$ is equivalent to $p ∧ q,$ where $⊕, eÎ\{∧, ∨\}$ then the ordered pair $(⊕, e)$ is $\sim .$
  • A
    $(∨, ∧)$
  • B
    $(∨, ∨)$
  • ✓
    $(∧, ∨)$
  • D
    $(∧, ∧)$
Answer
Correct option: C.
$(∧, ∨)$
View full question & answer→
MCQ 1281 Mark
The inverse of the statement $"$If a number is divisible by $4$ then it is also divisible by $2"$ is:
  • ✓
    If a number is not divisible by $4,$ then it is not divisible by $2.$
  • B
    If a number is divisible by $4,$ then it is always divisible by $2.$
  • C
    If a number is not divisible by $4,$ then it is divisible by $2.$
  • D
    None of the above.
Answer
Correct option: A.
If a number is not divisible by $4,$ then it is not divisible by $2.$
a number is not divisible by $4$ is the negation of the hypothesis a number is divisible by $4$, and it is not divisible by $2$ is the negation of the conclusion it is also divisible by $2.$
View full question & answer→
MCQ 1291 Mark
Which of the following is not negation of statement $“$Sum of $2$ and $3$ is greater than $4”\ ?$
  • ✓
    Sum of $2$ and $3$ is smaller than $4$
  • B
    Sum of $2$ and $3$ is smaller than or equal to $4$
  • C
    Sum of $2$ and $3$ is not greater than $4$
  • D
    It is false that sum of $2$ and $3$ is greater than $4$
Answer
Correct option: A.
Sum of $2$ and $3$ is smaller than $4$
Negation of greater is ‘not greater’. ‘Not greater’ means either smaller than or equal to.
So, “Sum of $2$ and $3$ is smaller than or equal to $4”, “$Sum of $2$ and $3$ is not greater than $4”, “$Sum of $2$ and $3$ is not greater than $4”$ are negation of the given statement.
And $“$Sum of $2$ and $3$ is smaller than $4”$ is not the negation of given statement as it should include equal to also.
View full question & answer→
MCQ 1301 Mark
A sentence is called a mathematically accepted statement if
  • A
    It’s true.
  • ✓
    It’s either true or false but not both.
  • C
    It’s false.
  • D
    It’s neither true or false.
Answer
Correct option: B.
It’s either true or false but not both.
View full question & answer→
MCQ 1311 Mark
Let $p, q, r$ denote arbitrary statements. Then the logically equivalent of the statement $p \Rightarrow (q ∨ r)$ is $\sim .$
  • A
    $(p ∨ q) \Rightarrow r$
  • ✓
    $(p \Rightarrow q)\ ∨\ (p \Rightarrow r)$
  • C
    $(p \Rightarrow ~q)\ ∧\ (p \Rightarrow r)$
  • D
    $(p \Rightarrow q) ∧ (p \Rightarrow ~r)$
Answer
Correct option: B.
$(p \Rightarrow q)\ ∨\ (p \Rightarrow r)$
View full question & answer→
MCQ 1321 Mark
In the truth table for the statement $( \sim p \rightarrow \sim q) ∧ ( \sim q \rightarrow \sim p),$ the last column has the truth value in the following order is.
  • A
    $\text{TTTF}$
  • B
    $\text{FTTF}$
  • C
    $\text{TFFT}$
  • ✓
    $\text{TTTT}$
Answer
Correct option: D.
$\text{TTTT}$
View full question & answer→
MCQ 1331 Mark
Which of the following is a preposition?
  • A
    I am an advocate
  • ✓
    Delhi is on the Jupiter
  • C
    A half open door is half closed
  • D
    None of these
Answer
Correct option: B.
Delhi is on the Jupiter
View full question & answer→
MCQ 1341 Mark
The connective in the statement “Earth revolves around the Sun and Moon is a satellite of earth" is:
  • A
    or
  • B
    Earth
  • C
    Sun
  • ✓
    and
Answer
Correct option: D.
and
Given statement: Earth revolves around the Sun and Moon is a satellite of earth
Here, the connective word is “and.”
View full question & answer→
MCQ 1351 Mark
Here are some words translated from an artificial language
mie pie is blue light
mie tie is blue berry
aie tie is rasp berry
Which words could possibly mean "light fly"?
  • ✓
    Pie zie
  • B
    Pie mie
  • C
    Aie zie
  • D
    Aie mie
Answer
Correct option: A.
Pie zie
It is clear that pie means light.
So there can be only $2$ correct options, either pie zie or pie mie.
But mie means blue as it is common in the first two statements.
View full question & answer→
MCQ 1361 Mark
Which of the following statements is false?
  • A
    Delhi and Mumbai are cities of India
  • B
    Chandigarh is capital of Punjab and Haryana
  • ✓
    $81$ is a square and cube
  • D
    $16$ is even number and divisible by $8$
Answer
Correct option: C.
$81$ is a square and cube
Since Delhi and Mumbai both are cities in India so $“$Delhi and Mumbai are cities of India$”$ is true.
Since Chandigarh is the capital of both states Punjab and Haryana so $“$Chandigarh is capital of Punjab and Haryana$”$ is true.
Since $81$ is a square and not a cube so $“81$ is a square and cube$”$ is false.
Since $16$ is even number and is also divisible by $8$
so $“16$ is even number and divisible by $8”$ is true.
View full question & answer→
MCQ 1371 Mark
The negation of $q\ ∨ \sim (p ∧ r)$ is.
  • A
    $\sim q\ ∨ (p ∨ r)$
  • ✓
    $\sim q\ ∧\ (p ∧ r)$
  • C
    $q\ ∨ (p ∨ r)$
  • D
    $\sim q ∧ (p ∨ r)$
Answer
Correct option: B.
$\sim q\ ∧\ (p ∧ r)$
View full question & answer→
MCQ 1381 Mark
Which of the following statement is a conjunction.
  • A
    Ram and Shyam are friends
  • B
    Both Ram and Shyam are friends
  • C
    Both Ram and Shyam are enemies
  • ✓
    None of these
Answer
Correct option: D.
None of these
All the statements are conjunction.
View full question & answer→
MCQ 1391 Mark
Denial of a statement is called its:
  • ✓
    negation
  • B
    converse
  • C
    inverse
  • D
    truth value
Answer
Correct option: A.
negation
It is a fundamental concept that, denial of a mathematical statement is called its negation.
View full question & answer→
MCQ 1401 Mark
A rectangle is a quadrilateral and its four sides are equal. Which is not correct?
  • ✓
    A rectangle is a quadrilateral is false.
  • B
    A rectangle has four sides is true.
  • C
    A rectangle is a quadrilateral is true.
  • D
    A rectangle has all sided equal is false.
Answer
Correct option: A.
A rectangle is a quadrilateral is false.
A rectangle has four sides so it is a quadrilateral.
All the four sides are not equal as two are equal and other two are equal.
View full question & answer→
MCQ 1411 Mark
Which of the following is true?
  • A
    $p \Rightarrow q = \sim p \Rightarrow \sim q$
  • ✓
    $\sim (p \Rightarrow \sim q) = \sim p\ ∧ q$
  • C
    $\sim  (\sim p \Rightarrow \sim q) = \sim p ∧ q$
  • D
    $\sim (\sim p \Rightarrow q) = [\sim (p \Rightarrow q) ∧ \sim (q \Rightarrow p)]$
Answer
Correct option: B.
$\sim (p \Rightarrow \sim q) = \sim p\ ∧ q$
View full question & answer→
MCQ 1421 Mark
Choose the correct answer: Which of the following statement is a conjunction?
  • A
    Ram and Shyam are friends.
  • B
    Both Ram and Shyam are tall.
  • C
    Both Ram and Shyam are enemies.
  • ✓
    None of the above.
Answer
Correct option: D.
None of the above.
If two simple statements $p$ and $q$ are connected by the word ‘and’, then the resulting compound statement $p$ and $q$ is called a conjunction of $p$ and $q.$
Here, none of the given statement is conjunction.
View full question & answer→
MCQ 1431 Mark
Which of the following cannot be the negation of the statement “Delhi is in India”?
  • A
    Delhi is not in India.
  • B
    It is false that Delhi is in India.
  • ✓
    It is false that Delhi is not in India.
  • D
    It is not the case that Delhi is in India.
Answer
Correct option: C.
It is false that Delhi is not in India.
“Delhi is not in India”, “It is false that Delhi is in India”, “It is not the case that Delhi is in India” are negations of the given statement.
Negation of a statement can be formed by adding ‘it is false that’ or ‘it is not the case that’.
In statement “It is false that Delhi is not in India” two negation phrases are used which is wrong so it is not the negation statement.
View full question & answer→
MCQ 1441 Mark
There are $25$ days in a month. This is.
  • A
    an implication
  • B
    a quantifier
  • C
    a compound statement
  • ✓
    a statement
Answer
Correct option: D.
a statement
View full question & answer→
MCQ 1451 Mark
Which of the following proposition is a tautology?
  • A
    $\sim p\ ∧ (\sim p\ ∨ \sim q)$
  • B
    $\sim q ∧ (\sim p\ ∨ \sim q)$
  • C
    $(\sim p\ ∨ \sim q) ∧ (p\ ∨ \sim q)$
  • ✓
    $(\sim p\ ∨ \sim q) ∨ (p\ ∨ \sim q)$
Answer
Correct option: D.
$(\sim p\ ∨ \sim q) ∨ (p\ ∨ \sim q)$
View full question & answer→
MCQ 1461 Mark
The symbolic form of a statement "It is not true that Kiran passed therfore he is said' is.
  • A
    $(\sim p \rightarrow q)$
  • ✓
    $(p \rightarrow q)$
  • C
    $\sim (p \rightarrow \sim q)$
  • D
    $\sim ( p \leftrightarrow q)$
Answer
Correct option: B.
$(p \rightarrow q)$
View full question & answer→
MCQ 1471 Mark
Which one of the following is a tautology?
  • ✓
    $(p ∧ (p \rightarrow q)) \rightarrow q$
  • B
    $q \rightarrow (p ∧ (p \rightarrow q))$
  • C
    $p ∧ (p ∨ q)$
  • D
    $p ∨ (p ∧ q)$
Answer
Correct option: A.
$(p ∧ (p \rightarrow q)) \rightarrow q$
View full question & answer→
MCQ 1481 Mark
Which of the following is not a statement?
  • A
    $2$ is an even integer.
  • B
    $2 + 1 = 3.$
  • C
    The number $17$ is prime.
  • ✓
    $x + 3 = 10, \text{x ÎR.}$
Answer
Correct option: D.
$x + 3 = 10, \text{x ÎR.}$
View full question & answer→
MCQ 1491 Mark
Which statement is logically equivalent to "If Yoda cannot use a lightsaber then he cannot help Luke win the battle":
  • A
    Yoda cannot use a lightsaber and he will help Luke win the battle.
  • ✓
    If Yoda can help Luke win the battle then he can use a lightsaber.
  • C
    Yoda can use a lightsaber if and only if he can help Luke win the battle.
  • D
    Yoda cannot use a lightsaber and will not help Luke win the battle.
Answer
Correct option: B.
If Yoda can help Luke win the battle then he can use a lightsaber.
A statement is logically equivalent to its contrapositive To form the contrapositive switch the "If" and "then" sections of the statement $\text{AND}$ insert $\text{"NOTs"}$ into each section Notice in this situation that inserting $\text{"NOTs"}$ turns the thoughts positive $($you are negating negative thoughts$).$
View full question & answer→
MCQ 1501 Mark
If $p$ and $q$ are mathematical statements, then in order to show that the statement $“p$ and $q”$ is true, we need to show that:
  • A
    The statement $p$ is true and the statement $q$ ement $p$ is true and the statement $q$ is not true.
  • B
    The statement $p$ is false and the statement $q$ is true.
  • C
    The statement $p$ is true and the statement $q$ is false.
  • ✓
    The statement $p$ is true and the statement $q$ is true.
Answer
Correct option: D.
The statement $p$ is true and the statement $q$ is true.
View full question & answer→
MCQ 1511 Mark
Which of the following is a statement?
  • A
    Today is Monday
  • B
    Tomorrow will be holiday
  • ✓
    If today is Tuesday then tomorrow will be Sunday
  • D
    There will be full moon tonight
Answer
Correct option: C.
If today is Tuesday then tomorrow will be Sunday
“Today is Monday”, “Tomorrow will be holiday”, “There will be full moon tonight” are not the statements because we are not sure which day or night we are talking about.
“If today is Tuesday then tomorrow will be Sunday” is a statement because we are sure that it is false.
Wednesday come after Tuesday so if today is Tuesday then tomorrow will be Wednesday.
View full question & answer→
MCQ 1521 Mark
Find the truth value of the compound statement, $4$ is the first composite number and $2 + 5 = 7.$
  • ✓
    $T$
  • B
    $F$
  • C
    Neither $T$ nor $F$
  • D
    Cannot be determined
Answer
Correct option: A.
$T$
The given statement is True, as $4$ is the first composite number.
Also $2 + 5 = 7$
View full question & answer→
MCQ 1531 Mark
The only statement among the following that is a tautology is.
  • A
    $A ∧ (A ∨ B)$
  • B
    $A ∨ (A ∧ B)$
  • ✓
    $[A ∧ (A \rightarrow B)] \rightarrow B$
  • D
    $B \rightarrow [A ∧ (A \rightarrow B)]$
Answer
Correct option: C.
$[A ∧ (A \rightarrow B)] \rightarrow B$
View full question & answer→
MCQ 1541 Mark
Which of the following statement is false?
  • A
    $24$ is even number or odd number
  • B
    $15$ is prime or divisible by $3$
  • C
    $71$ is odd number or prime
  • ✓
    Japan or China is in India
Answer
Correct option: D.
Japan or China is in India
$24$ is even number so $“24$ is even number or odd number” is correct.
$15$ is divisible by $3$ so $“15$ is prime or divisible by $3”$ is true.
$71$ is prime as well as odd so $“71$ is odd number or prime” is true.
Neither Japan nor China is in India so “Japan or China is in India” is false.
View full question & answer→
MCQ 1551 Mark
The contrapositive of the statement If $p$ then $q$ is:
  • A
    If $q$, then $p.$
  • B
    If $p,$ then $\sim  q.$
  • ✓
    If $\sim  q,$ then $\sim  p.$
  • D
    If $\sim p,$ then $ \sim  q.$
Answer
Correct option: C.
If $\sim  q,$ then $\sim  p.$
The contrapositive of the statement If $p,$ then $q,$ is If $\sim  q,$ then $\sim  p.$
View full question & answer→
MCQ 1561 Mark
Let $p$ and $q$ be two propositions. Then the contrapositive of the implication $p \rightarrow q$ is.
  • ✓
    $\sim q \rightarrow \sim p$
  • B
    $\sim p \rightarrow \sim q$
  • C
    $\sim q \rightarrow p$
  • D
    $p \rightarrow q$
Answer
Correct option: A.
$\sim q \rightarrow \sim p$
View full question & answer→
MCQ 1571 Mark
The converse of the statement if a number is divisible by $10,$ then it is divisible by $5$ is.
  • A
    If a number is not divisible by $5,$ then it is not divisible by $10$
  • B
    If a number is divisible by $5,$ then it is not divisible by $10$
  • C
    If a number is not divisible by $5,$ then it is divisible by $10$
  • ✓
    If a number is divisible by $5,$ then it is divisible by $10$
Answer
Correct option: D.
If a number is divisible by $5,$ then it is divisible by $10$
Given, statement is if a number is divisible by $10,$ then it is divisible by $5$
Now, converse of the statement is:
If a number is divisible by $5,$ then it is divisible by $10$
View full question & answer→
MCQ 1581 Mark
Choose the correct answer:
The negation of the statement.
“Rajesh or Rajni lived in Bangalore” is.
  • A
    Rajesh did not live in Bangalore or Rajni lives in Bangalore.
  • B
    Rajesh lives in Bangalore and Rajni did not live in Bangalore.
  • ✓
    Rajesh did not live in Bangalore and Rajni did not live in Bangalore.
  • D
    Rajesh did not live in Bangalore or Rajni did not live in Bangalore.
Answer
Correct option: C.
Rajesh did not live in Bangalore and Rajni did not live in Bangalore.
We have, $p:$ Rajesh or Rajni lived in Bangalore.
and $q:$ Rajesh lived in Bangalore.
$r:$ Rajni lived in Bangalore.
$\sim q:$ Rajesh did not live in Bangalore.
$\sim r.$ Rajni did not live in Bangalore.
$\sim  (q v r):$ Rajesh did not live in Bangalore and Rajni did not live in Bangalore.
View full question & answer→
MCQ 1591 Mark
Which is logically equivalent to "If today is Sunday Matt cannot play hockey"?
  • A
    Today is Sunday and Matt can play hockey.
  • ✓
    If Matt plays hockey then today is not Sunday.
  • C
    Today is Sunday and Matt cannot play hockey.
  • D
    Today is not Sunday if and only if Matt plays hockey.
Answer
Correct option: B.
If Matt plays hockey then today is not Sunday.
Matt can play Hockey on any day other than Sunday.
View full question & answer→
MCQ 1601 Mark
If $p \Rightarrow (\text{q ∨ r})$ is false, then the truth values of $\text{p, q, r,}$ are respectively.
  • ✓
    $\text{T, F, F}$
  • B
    $\text{F, F, F}$
  • C
    $\text{F, T, T}$
  • D
    $\text{T, T, F}$
Answer
Correct option: A.
$\text{T, F, F}$
View full question & answer→
MCQ 1611 Mark
Which of the following is not a statement?
  • A
    $2$ is an even integer.
  • B
    $2 + 1= 3.$
  • C
    The number $17$ is prime.
  • ✓
    $x + 3 = 10, x Î R.$
Answer
Correct option: D.
$x + 3 = 10, x Î R.$
View full question & answer→
MCQ 1621 Mark
The connective in the statement $2 + 7 > 9$ or $2 + 7 < 9$ is.
  • A
    And
  • ✓
    Or
  • C
    $ > $
  • D
    $ < $
Answer
Correct option: B.
Or
Given, statement is $2 + 7 > 9$ or $2 + 7 < 9$
Here, connective is or.
It connects two statement $2 + 7 > 9, 2 + 7 < 9.$
View full question & answer→
MCQ 1631 Mark
The contrapositive of the statement 'I go to school if it does not rain' is:
  • A
    If it rains, I do not go to school.
  • ✓
    If I do not go to school, it rains.
  • C
    If it rains, I go to school.
  • D
    If i go to school, it rains.
Answer
Correct option: B.
If I do not go to school, it rains.
In the given statement, let p denote the part "it does not rain"
Aand q denote the part "i go to school"
So the given statement is $p \rightarrow q$
Now for a contrapositive statement, by definition we have
$(p \rightarrow q) \leftrightarrow (\sim q \rightarrow \sim p)$
So $\sim q$ means "i do not go to school"
and $\sim p$ means "it rains"
$\sim q \rightarrow \sim p$ means "if i do not go to school, it rains".
View full question & answer→
MCQ 1641 Mark
The inverse of the statement "If it is raining then the grass is wet":
  • ✓
    "If it is not raining then the grass is not wet".
  • B
    "If it is raining then the grass is not wet".
  • C
    "If it is not raining then the grass is wet".
  • D
    None of these.
Answer
Correct option: A.
"If it is not raining then the grass is not wet".
$p \rightarrow q$
Inverse is $\sim p \rightarrow \sim q$
$\Rightarrow$ Inverse of:
It it is raining then the grass is wet is:
If it is not raining then the grass is not wet.
View full question & answer→
MCQ 1651 Mark
$p ∧ (q ∧ r)$ is logically equivalent to.
  • A
    $(p ∨ q) ∧ r$
  • ✓
    $(p ∧ q) ∧ r$
  • C
    $p \rightarrow (q ∧ r)$
  • D
    $(p ∨ q) ∨ r$
Answer
Correct option: B.
$(p ∧ q) ∧ r$
View full question & answer→
MCQ 1661 Mark
The negation of the Boolean expression $p ∨ (\sim p ∧ q)$ is equivalent to $\sim$
  • A
    $p ∧ \sim q$
  • ✓
    $\sim p ∧ \sim q$
  • C
    $\sim p ∨ \sim q$
  • D
    $\sim p ∨ q$
Answer
Correct option: B.
$\sim p ∧ \sim q$
View full question & answer→
MCQ 1671 Mark
If $p \Rightarrow (~p ∨ q)$ is false, the truth values of $p$ and $q$ are respectively.
  • A
    $F, T$
  • B
    $F, F$
  • C
    $T, T$
  • ✓
    $T, F$
Answer
Correct option: D.
$T, F$
View full question & answer→
MCQ 1681 Mark
The contra$-$positive of the statement if $p$ then $q$ is:
  • A
    If $\sim p$ then $q$
  • B
    If $p$ then $\sim q$
  • C
    If $q$ then $p$
  • ✓
    If $\sim q$ then $\sim p$
Answer
Correct option: D.
If $\sim q$ then $\sim p$
Given statement is if $p$ then $q$
Now, contra$-$positive of the statement is:
If $\sim q$ then $\sim p$
View full question & answer→
MCQ 1691 Mark
If the coefficient of variation is $100$ the mean of the data is $25,$ then find the standard deviation.
  • A
    $5$
  • B
    $10$
  • C
    $15$
  • ✓
    $25$
Answer
Correct option: D.
$25$
Coefficient of Variance $ = (\frac{\text{Standard Deviation}}{\text{Mean}}) \times 100$
$ \Rightarrow$ Standard Deviation $= 25.$
View full question & answer→
MCQ 1701 Mark
Which of the following statements is the inverse of "If it rains, then I do not go fishing."?
  • A
    If I go fishing, then it does not rain.
  • B
    If I do not go fishing, then it rains.
  • ✓
    If it does not rain, then I go fishing.
  • D
    None of these.
Answer
Correct option: C.
If it does not rain, then I go fishing.
Therefore, the reason comes after the assertion.
Then, the inverse of the expression "if it rains, then I do not go fishing " is:
If I go fishing, then it does not rain.
View full question & answer→
MCQ 1711 Mark
Choose the correct answer:
The contrapositive of the statement.
“If $7$ is greater than $5$, then $8$ is greater than $6”$ is.
  • A
    If $8$ is greater than $6,$ then $7$ is greater than $5.$
  • B
    If $8$ is not greater than $6,$ then $7$ is greater than $5.$
  • ✓
    If $8$ is not greater than $6,$ then $7$ is not greater than $5.$
  • D
    If $8$ is greater than $6$, then $7$ is not greater than $5.$
Answer
Correct option: C.
If $8$ is not greater than $6,$ then $7$ is not greater than $5.$
Letp: $7$ is greater than $5.$
and $q: 8$ is greater than $6.$
$\therefore p \rightarrow q$
$\sim p: 7$ is not greater than $5.$
$\sim q: 8$ is not greater than $6.$
$(\sim q) \rightarrow (\sim p)$ i.e., if $8$ is not greater than $6,$ then $7$ is not greater than $5.$
View full question & answer→
MCQ 1721 Mark
If $p$ then $q$ means if $p$ is $...........$ then $q$ must be $...........$
  • ✓
    True, true
  • B
    True, false
  • C
    False, false
  • D
    False, true
Answer
Correct option: A.
True, true
If $p$ then $q$ means if $p$ is true then $q$ must be true.
It says nothing when $p$ is false.
If $p$ is false then $q$ might be true or false.
View full question & answer→
MCQ 1731 Mark
If $p \rightarrow (~p ∨ ~q)$ is false, then the truth values of $p$ and $q$ are respectively.
  • A
    $T, F$
  • B
    $F, F$
  • C
    $F, T$
  • ✓
    $T, T$
Answer
Correct option: D.
$T, T$
View full question & answer→
MCQ 1741 Mark
If $p$ then $q$ means if $p$ is $...........$ then $q$ must be $...........$
  • ✓
    true, true
  • B
    true, false
  • C
    false, false
  • D
    false, true
Answer
Correct option: A.
true, true
If $p$ then $q$ means if $p$ is true then $q$ must be true.
It says nothing when $p$ is false.
If $p$ is false then q might be true or false.
View full question & answer→
MCQ 1751 Mark
Which of the following is the inverse of the proposition: “If a number is a prime then it is odd.”
  • A
    If a number is not a prime then it is odd
  • ✓
    If a number is not a prime then it is odd
  • C
    If a number is not odd then it is not a prime
  • D
    If a number is not odd then it is a prime
Answer
Correct option: B.
If a number is not a prime then it is odd
View full question & answer→
MCQ 1761 Mark
If $p$ then $q$ means $...........$
  • A
    If $q$ then $p$
  • ✓
    $p \Rightarrow q$
  • C
    $q \Rightarrow p$
  • D
    $q$ only if $p$
Answer
Correct option: B.
$p \Rightarrow q$
If $p$ then $q$ means $p$ implies $q$
i.e. $p \Rightarrow q.$
This does not mean $q \Rightarrow p.$
$Q$ only if $p$ means $q \Rightarrow p.$
View full question & answer→
MCQ 1771 Mark
Which of the following is not a negation of the statement A natural number is greater than zero.
  • A
    A natural number is not greater than zero
  • B
    It is false that a natural number is greater than zero
  • ✓
    It is false that a natural number is not greater than zero
  • D
    None of these
Answer
Correct option: C.
It is false that a natural number is not greater than zero

Given statement is:
A natural number is greater than zero Negation of the statement:
A natural number is not greater than zero
It is false that a natural number is greater than zero
View full question & answer→
MCQ 1781 Mark
Which of the following is a statement.
  • A
    $x$ is a real number
  • B
    Switch of the fan
  • ✓
    $6$ is a natural number
  • D
    Let me go
Answer
Correct option: C.
$6$ is a natural number
The statement $6$ is a natural number is true.
So, it is a statement.
View full question & answer→
MCQ 1791 Mark
Choose the correct answer:
The converse of the statement.
“If sun is not shining, then sky is filled with clouds” is.
  • ✓
    If sky is filled with clouds, then the sun is not shining.
  • B
    If sun is shining, then sky is filled with clouds.
  • C
    If sky is clear, then sun is shining.
  • D
    If sun is not shining, then sky is not filled with clouds.
Answer
Correct option: A.
If sky is filled with clouds, then the sun is not shining.
Let $p:$ Sun is not shining.
$q:$ Sky is filled with clouds.
So, the converse of the statement $p \rightarrow q$ is $q \rightarrow p.$
i.e., If Sky is filled with clouds, then the Sun is not shining.
View full question & answer→
MCQ 1801 Mark
Which of the following cannot be the negation of the statement “All angles are equal in equilateral triangle”?
  • A
    There is at least one angle different in equilateral triangle.
  • B
    It is false that all angles are equal in equilateral triangle.
  • C
    It is not the case that all angles are equal in equilateral triangle.
  • ✓
    All angles are unequal in equilateral triangle.
Answer
Correct option: D.
All angles are unequal in equilateral triangle.
Negation of all angles is ‘not all angles’. So, negation of the given statement is “There is at least one angle different in equilateral triangle”, “It is false that all angles are equal in equilateral triangle”, “It is not the case that all angles are equal in equilateral triangle”. But “All angles are unequal in equilateral triangle” cannot be the negation of given statement as this does not include isosceles triangles.
View full question & answer→
Generate Paper FreeAll Mathematical Reasoning topics