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CBSE Questions for Class 11 Engineering Maths Mathematical Reasoning Quiz 4 - MCQExams.com

State the following statement is True or False
If p,q,r are statements with truth values T, F, T respectively, then the truth value of (pq)rp, is T
  • True
  • False
The contrapositive of (pq)r is
  • r(pq)
  • r(pq)
  • r⇒∼pq
  • R(qr)
Which of the following is/are a statement?
  • Give me a glass of water.
  • Asia is continent.
  • The earth revolves round sun.
  • The number 6 has two prime factor 2,3.
State the following statement is True or False
If p,q,r are statements, with truth values T, F, T respectively, then the truth value of (pq)rp is T
  • True
  • False
If p(qr) is false, then the truth values of p,q,r are respectively
  • T, F, F
  • F, F, F
  • F, T, T
  • T, T, F
If x = 5 and y = -2, then x-2y = 9. The contrapositive of this statement is/are
  • If x-2y \neq 9, then x \neq 5 or y \neq 2.
  • If x-2y \neq 9, then x \neq 5 and y \neq -2.
  • If x-2y = 9, then x = 5 and y = -2.
  • none of these.
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.
  • Either I will not become a teacher or I will not open a school.
  • Neither I will become a teacher nor I will open a school.
  • I will not become a teacher or I will open a school.
If x = 5 and y = 2 then x - 2y = 9. The contrapositive of this statement is
  • If x -2y \neq 9 then  x \neq 5  or  y \neq 2
  • If x -2y \neq 9 then  x \neq 5 and y \neq - 2
  • If x - 2y = 9  then  x = 5 and y = -2
  • none of these.
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
  • May be true
  • False
  • May be false
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) ?
  • (i) and (ii)
  • (ii) and (iii)
  • (iii) and (iv)
  • All of these
The contrapositive of p\rightarrow (\sim q\rightarrow \sim r) is equivalent to
  • (\sim q\wedge r)\rightarrow \sim p
  • (q\wedge \sim r)\rightarrow \sim p
  • p\rightarrow (\sim r\vee q)
  • p\wedge (q\vee r)
Which one of the following statements is not a false statement?
  • p: Each radius of a circle is a chord of the circle.
  • q: Circle is a particular case of an ellipse.
  • r:\>\displaystyle \sqrt{13} is a rational number.
  • s: The centre of a circle bisects each chord of the cirlce.
Consider the. following compound statement
(i) Mumbai is the capital of Rajasthan or Maharashtra,
(ii) \displaystyle \sqrt{3} is a rational number or an irrational number,
(iii) 125 is a multiple of 7 or 8
(iv) A rectangle is a quadrilateral or a regular hexagon.
Which of the above statements is not true?
  • (i)
  • (ii)
  • (iii)
  • (Iv)
The contrapositive of (\sim p\wedge q)\rightarrow \sim r is equivalent to
  • (p\wedge q)\rightarrow r
  • (p\wedge q)\vee r
  • r\rightarrow (p\vee \sim q)
  • none of these
The contrapositive of the statement "If you believe in yourself and are honest then you will get sucess" is
  • If you do not believe yourself and are dishonest then you will not get success.
  • If you do not believe yourself and are dishonest then you will get success.
  • 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
The converse of p \rightarrow (q \rightarrow r) is 
  • (q \wedge \sim r) \vee p
  • (\sim q \vee r)\vee p
  • (q \wedge \sim r) \wedge \sim p
  • (q \wedge \sim r) \wedge p
In the following letter sequence, some of the letters are missing. These are given in order as one of the alternatives below. Choose the correct alternative.
\alpha \beta _\alpha \alpha _\beta \beta \beta _\alpha \alpha \alpha \alpha _\beta \beta \beta ...
  • \alpha \beta \beta \alpha
  • \beta \alpha \beta \alpha
  • \alpha \alpha \alpha \beta
  • \alpha \beta \alpha \beta
The negation of the statement q \vee  (p \wedge \sim r) is equivalent to 
  • \sim q \wedge(p \rightarrow r)
  • \sim q \vee \sim(p \rightarrow r)
  • q \wedge (\sim p \wedge r)
  • None of these.
The converse of p \rightarrow (q \rightarrow r) is
  • (q \wedge \sim r) \vee p
  • (\sim q \vee r) \vee p
  • (q \wedge \sim r) \wedge \sim p
  • (q \wedge \sim r) \wedge p
The contrapositive of \sim p \rightarrow ( q \rightarrow \sim r) is
  • (~q \wedge r) \rightarrow ~p
  • (q \rightarrow r) \rightarrow~p
  • (q \vee ~r) \rightarrow ~ p
  • None of these
The negative of the statement "If a number is divisible by 15 then it is divisible by 5 or 3"
  • If a number is not divisible by 15, then it is not divisible by 5 and 3
  • A number is divisible by 15 and it is not divisible by 5 or 3
  • 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
If statements p, q, r have truth values T, F, T respectively then which of the following statement is true 
  • (p \rightarrow q) \wedge r
  • (p \rightarrow q) \vee \sim r
  • (p \wedge q)\vee (q \wedge r)
  • (p \rightarrow q) \rightarrow r
The contrapositive of p \rightarrow (\sim q \rightarrow \sim r) is 
  • (\sim q\wedge r) \rightarrow \sim p
  • (q \rightarrow r) \rightarrow \sim p
  • ( q \vee \sim r) \rightarrow \sim p
  • none of these.
Negation of \displaystyle q \vee \sim \left ( p\wedge r \right ) is
  • \displaystyle \sim q\wedge \sim \left ( p\wedge r \right )
  • \displaystyle \sim q\wedge \left ( p\wedge r \right )
  • \displaystyle \sim q\vee \left ( p\wedge r \right )
  • None of these
Find the truth value of the compound statement, 4 is the first composite number and 2+5=7.
  • T
  • F
  • Neither T nor F
  • cannot be determined
The negation of the statement "2 + 3 = 5" and "8 < 10" is
  • 2 + 3 \neq 5 and 8\nless 10
  • 2 + 3 \neq 5 or 8 > 10
  • 2 + 3 \neq 5 or 8 \ngeqslant 10
  • None of these
Find the quantifier which best describes the variable of the open sentence x^2+2\ge0
  • Universal.
  • Existential.
  • Neither (a) nor (b).
  • Does not exist.
The inverse of the statement (p \wedge \sim q)  \rightarrow r is
  • \sim (p \vee \sim q) \rightarrow \sim r
  • (\sim p \wedge \sim q) \rightarrow \sim r
  • (\sim p \vee q) \rightarrow \sim r
  • None of these.
What is the truth value of the statement 'Two is an odd number iff 2 is a root of x^2+2=0'?
  • T
  • F
  • Neither T nor F
  • Cannot be determined
The negative of the statement "If a number is divisible by 15 then it is divisible by 5 or 3"
  • if a number is divisible by 15 then it is not divisible by 5 and 3
  • a number is divisible by 15 and it is not divisible by 5 or 3
  • a number is 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
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