# Discrete Mathematics | Week 3

## Quiz

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

a. Ram does not like ice cream and Sudha does not like ice-cream

Explanation

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}

b. I , II and III

Explanation

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

b. A ∨ ¬A

Explanation

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

a. Reena likes travelling less frequently

Explanation

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

d.  (p ∧ q) → r

Explanation

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

c. ¬p ⊻ q

Explanation

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?

a.   F , F

Explanation

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

d. ¬p ∧ ¬q

Explanation

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

b. Gautam will play cards

Explanation

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

c. F , T

Explanation 0 