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

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

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Answer: c

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

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

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Answer: d

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

The compound statement A v ~(A ∧ B).

a) True

b) False

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Answer: a

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

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

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Answer: b

Explanation: Definition of De–Morgan’s Law.

. 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)

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Answer: b

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

~ A v ~ B is logically equivalent to?

a) ~ A → ~ B

b) ~ A ∧ ~ B

c) A → ~B

d) B V A

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Answer: c

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

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

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Answer: a

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

Which of the following satisfies commutative law?

a) ∧

b) v

c) ↔

d) All of the mentioned

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Answer: d

Explanation: All of them satisfies commutative law.

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

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Answer: a

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

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

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Answer: a

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