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
$\text{F, T, T}$
AnswerCorrect 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 $9.$
AnswerCorrect 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
AnswerCorrect 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
AnswerCorrect 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:
Answerd. 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
- C
- ✓
Answer$8$ 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 $2$
AnswerCorrect 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.
- ✓
- B
- C
neither a tautology nor contradiction
- D
cannot come any conclusion
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
- ✓
Answer$(p$ 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
- B
- ✓
$3$ is a prime number
- D
AnswerCorrect 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
- ✓
- C
false if $r$ is true
- D
false if $q$ is false
View full question & answer→MCQ 121 Mark
Which of the following is a statement?
- A
- ✓
$11$ comes after $12$
- C
India is a beautiful country
- D
AnswerCorrect 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.
AnswerCorrect 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
$\sim r \rightarrow (\sim p\ ∧ \sim q)$
AnswerCorrect 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
- ✓
Answer$(p$ 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
$1.64$
AnswerCorrect 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.
AnswerCorrect 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 $q$
AnswerCorrect 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
AnswerCorrect 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 $p \rightarrow q?$
AnswerCorrect 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
- ✓
$6$ is a natural number.
- D
AnswerCorrect 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 $3.$
AnswerCorrect 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
$\text{F, F, F}$
AnswerCorrect option: B. $\text{T, F, F}$
View full question & answer→MCQ 241 Mark
Which of the following is the conditional $p \rightarrow q.$
AnswerCorrect 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
$\sim p ∨ q$
AnswerCorrect option: B. $\sim p ∧ q$
View full question & answer→MCQ 261 Mark
Logical equivalent proposition to the proposition $\sim (p ∨ q)$ is.
AnswerCorrect 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.
AnswerA 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.
AnswerCorrect 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.
AnswerCorrect 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.
- ✓
AnswerWhen 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.
AnswerCorrect 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.
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 $q$
AnswerCorrect 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
$q, q$
AnswerCorrect 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 $............$
AnswerCorrect 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?
AnswerOf 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?
AnswerThe 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
- C
- ✓
If its raining then there must be cloud in the sky.
AnswerCorrect 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
- D
He is not rich and happy.
AnswerCorrect 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
AnswerCorrect 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
$\text{F, T, F}$
- ✓
$\text{T, T, F}$
AnswerCorrect 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.
AnswerCorrect 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 $2$
AnswerCorrect 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 $...........$
AnswerThe 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.
AnswerCoefficient 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 $(iv)$
- ✓
AnswerWe 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
$\text{F, F, F, T}$
AnswerCorrect 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 $..........$
AnswerIn 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 $2$
AnswerCorrect 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
$F, T$
AnswerCorrect option: C. $T, T$
View full question & answer→