This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “De-Morgan’s Laws”.

1. Which of the following statements is the negation of the statements “4 is odd or -9 is positive”?

a) 4 is even or -9 is not negative

b) 4 is odd or -9 is not negative

c) 4 is even and -9 is negative

d) 4 is odd and -9 is not negative

View Answer

Explanation: Using De Morgan’s Law ~(A V B) <-> ~A ∧ ~B.

2. Which of the following represents: ~A (negation of A) if A stands for “I like badminton but hate maths”?

a) I hate badminton and maths

b) I do not like badminton or maths

c) I dislike badminton but love maths

d) I hate badminton or like maths

View Answer

Explanation: De Morgan’s Law ~ (A ∧ B) <-> ~A V ~B.

3. The compound statement A v ~(A ∧ B) is always

a) True

b) False

View Answer

Explanation: Applying De-Morgan’s law we get A v ~ A Ξ Tautology.

4. Which of the following are De-Morgan’s law

1) P ∧ (Q v R) Ξ ( P ∧ Q ) v ( P ∧ R )

2) ~(P ∧ R) Ξ ~P v ~R , ~(P v R) Ξ ~P ∧ ~R

3) P v ~P Ξ True , P ∧ ~P Ξ False

4) None of the mentioned

View Answer

Explanation: Definition of De –Morgan’s Law.

5. What is the dual of (A ∧ B) v ( C ∧ D) ?

a) (A V B) v ( C v D)

b) (A V B) ^ ( C v D)

c) (A V B) v ( C ∧ D)

d) (A ∧ B) v ( C v D)

View Answer

Explanation: In dual ∧ is replaced by v and vice – versa.

6. ~ A v ~ B is logically equivalent to

a) ~ A → ~ B

b) ~ A ∧ ~ B

c) A → ~B

d) B V A

View Answer

Explanation: By identity A → B Ξ ~A V B.

7. Negation of statement (A ∧ B) → (B ∧ C)

a) (A ∧ B) →(~B ∧ ~C)

b) ~(A ∧ B) v ( B v C)

c) ~(A →B) →(~B ∧ C)

d) None of the mentioned

View Answer

Explanation: ~(A →B) Ξ A ∧ ~B using this we can easily fetch the answer.

8. Which of the following satisfies commutative law?

a) ∧

b) v

c) <->

d) All of the mentioned

View Answer

Explanation: All of them satisfies commutative law.

9. If the truth value of A v B is true, then truth value of ~A ∧ B can be

a) True if A is false

b) False if A is false

c) False if B is true and A is false

d) None of the mentioned

View Answer

Explanation: If A is false then both the condition are obeyed.

10. If P is always against the testimony of Q ,then the compound statement P→(P v ~Q) is a

a) Tautology

b) Contradiction

c) Contingency

d) None of the mentioned

View Answer

Explanation: Since either hypothesis is false or both (hypothesis as well as conclusion) are true.

**Sanfoundry Global Education & Learning Series – Discrete Mathematics.**

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