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 $x + a < y + a.$
AnswerCorrect 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 $q$
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 531 Mark
The method $(s)$ that are used to check the validity of statements is:
AnswerThe 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
$p ∨ q$
AnswerCorrect 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
$q, p$
AnswerCorrect 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
- ✓
$6$ is a natural number
- D
AnswerCorrect 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.
AnswerCorrect 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.
AnswerCorrect 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
$\text{T, T, F}$
AnswerCorrect 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 $9$
AnswerCorrect 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.
AnswerCorrect 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?
MCQ 631 Mark
The proposition $(p \rightarrow \sim p) ∧ (\sim p \rightarrow p)$ is
- ✓
- B
a contradiction and a tautology
- C
neither a contradiction nor a tautolog
- D
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 $2$
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. $q ⇒ p.$
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
- ✓
- C
May or may not be statements
- D
AnswerSentence 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
AnswerCorrect 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
AnswerCorrect 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
AnswerCorrect 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
- B
An ellipse is not a circle.
- ✓
A circle is not an ellipse.
- D
AnswerCorrect 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
AnswerCorrect 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?
AnswerCorrect 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 $\sim q.$
AnswerCorrect 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.
AnswerConnective 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
AnswerCorrect 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.
AnswerCorrect 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.
View full question & answer→MCQ 771 Mark
Which of the following pairs is logically equivalent?
- A
- B
- C
- ✓
Conditional, Contrapositive
AnswerCorrect 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
$q, p$
AnswerCorrect 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.
AnswerCorrect 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?
AnswerCorrect 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
$(\sim p\ Λ\ \sim q) ∨ (q\ Λ \sim r)$
AnswerCorrect 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.
AnswerCorrect 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
$\text{T, T, T, T}$
AnswerCorrect option: C. $\text{T, F, F, T}$
View full question & answer→MCQ 841 Mark
A sentence is called statement if it is $...............$
- A
- B
- ✓
Either true or false but not both
- D
AnswerCorrect 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
AnswerIn $‘2 + 7 > 9$ 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 $p$
AnswerCorrect 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 $3.$
AnswerCorrect 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:
AnswerA 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.
AnswerCorrect 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.
AnswerCorrect 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.
AnswerCorrect 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 $x + a < y + a.$
AnswerCorrect 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
AnswerCorrect 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.
AnswerCorrect 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.
AnswerCorrect 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?
AnswerSmoking 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.
AnswerCorrect 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
- ✓
- D
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
$\text{FFFT}$
AnswerCorrect 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
AnswerCorrect 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→