# Discrete Mathematics Week 3 NPTEL

**These are the solution of Discrete Mathematics Week 3 NPTEL Assignment 3 Answers**

Course name: Discrete Mathematics

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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

**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

**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

**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

**Answer: Reena likes travelling**

**These are the solution of Discrete Mathematics Week 3 NPTEL Assignment 3 Answers**

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

(p ∧ q) ∨ r

(p ∨ q) → r

p → q) → r

(p ∧ q) → r

**Answer: (p ∧ q) → r**

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

¬q ∧¬p

¬q ⊻¬p

¬p ⊻ q

¬q ∨¬p

**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

**Answer: F F**

**These are the solution of Discrete Mathematics Week 3 NPTEL Assignment 3 Answers**

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

¬p ∧ q

¬q

p ∨ q

¬p ∧ ¬q

**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 may not play cards

D. None of the above

**Answer: B. 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

**Answer: C. F T**

**These are the solution of Discrete Mathematics Week 3 NPTEL Assignment 3 Answers**

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