Engineering Questions with Answers - Multiple Choice Questions

# MCQs on Logics and Proofs – De-Morgan’s Laws

1 - Question

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

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

2 - Question

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

Explanation: De Morgan’s Law ~ (A ∧ B) ↔ ~A V ~B.

3 - Question

The compound statement A v ~(A ∧ B).
a) True
b) False

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

4 - Question

Which of the following is De-Morgan’s law?
a) P ∧ (Q v R) Ξ (P ∧ Q) v (P ∧ R)
b) ~(P ∧ R) Ξ ~P v ~R, ~(P v R) Ξ ~P ∧ ~R
c) P v ~P Ξ True, P ∧ ~P Ξ False
d) None of the mentioned

Explanation: Definition of De–Morgan’s Law.

5 - Question

. 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)

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

6 - Question

~ A v ~ B is logically equivalent to?
a) ~ A → ~ B
b) ~ A ∧ ~ B
c) A → ~B
d) B V A

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

7 - Question

Negation of statement (A ∧ B) → (B ∧ C) is _____________
a) (A ∧ B) →(~B ∧ ~C)
b) ~(A ∧ B) v ( B v C)
c) ~(A →B) →(~B ∧ C)
d) None of the mentioned

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

8 - Question

Which of the following satisfies commutative law?
a) ∧
b) v
c) ↔
d) All of the mentioned

Explanation: All of them satisfies commutative law.

9 - Question

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

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

10 - Question

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