1. Let p: Ram likes ice cream or Sudha likes toffee Negation of the statement p is?

• • • Ram does not like ice cream and Sudha does not like ice-cream

    • Ram does not like ice cream or Sudha does not like ice-cream

    • Ram does not like ice cream and Sudha likes ice-cream

    • Ram does not like ice cream or Sudha likes ice-cream

Correct Answer : Ram does not like ice cream and Sudha does not like ice-cream

2. Which of the following statement(s) is/are true?

I. The sentence, “Rajesh is a hardworking man” - is a statement

II. 9 is not a prime number

III. Cardinality of 𝐴 ∪ 𝐵 is 5, where, 𝐴={1,2,3} 𝐵={2,7,8}

• I and III

• I II and III

• II and III

• Only II

Correct Answer : II and III

3. If A is any statement, then which of the following is a tautology?

• • • A ∨ F

    • A ∨ ¬A

    • A ∧ F

    • A ∧ T

Correct Answer : A ∨ ¬A

4. “It is not that I don't like travelling”, said Reena, what does Reena mean?

• Reena likes travelling less frequently

• Reena does not likes travelling

• Reena likes travelling

• Reena does not likes travelling sometimes

Correct Answer : Reena likes travelling

5. (p → r) ∨ (q → r) is logically equivalent to

• (p ∧ q) ∨ r

• (p ∨ q) → r

• p → q) → r

• (p ∧ q) → r

Correct Answer : (p ∧ q) → r

6. (¬p ⊻ q) ∨ ( ¬q ∧¬p) is equivalent to

• ¬q ∧¬p

• ¬q ⊻¬p

• ¬p ⊻ q

• ¬q ∨¬p

Correct Answer : ¬p ⊻ q

7. If the truth value of s is True, where s is ¬((¬q ∧ ¬p) → p) then the truth value of p and q are respectively?

• F F

• T T

• T F

• F T

Correct Answer : F F

8. ¬(p ∨ q) ∨ (¬p ∧ ¬q) is logically equivalent to

• ¬p ∧ q

• ¬q

• p ∨ q

• ¬p ∧ ¬q

Correct Answer : ¬p ∧ ¬q

9. What can we infer from the below statement?

q: Gautam will go for a long drive to Mahabaleshwar or he will play cards

r: Gautam did not go to Mahabaleshwar

A. Gautam will not play cards

B. Gautam will play cards

C. Gautam maynot play cards

D. None of the above

Correct Answer : Gautam will play cards

10. If (¬p ⇒ ¬q) is false then what is the truth value of p and q?

A. T T

B. T F

C. F T

D. F F

Correct Answer : F T

WEEK-3 DETAILED SOLUTION