### 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

3. If A is any statement, then which of the following is a tautology?
A ∨ F
A ∨ ¬A
A ∧ F
A ∧ T

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

#### 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

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

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

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

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

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