Discrete Mathematics Questions and Answers – Logics and Proofs – De-Morgan’s Laws

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Logics and Proofs – 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
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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
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3. The compound statement A v ~(A ∧ B).
a) True
b) False
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4. 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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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)
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6. ~ A v ~ B is logically equivalent to?
a) ~ A → ~ B
b) ~ A ∧ ~ B
c) A → ~B
d) B V A
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7. 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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8. Which of the following satisfies commutative law?
a) ∧
b) v
c) ↔
d) All of the mentioned
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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
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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
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Sanfoundry Global Education & Learning Series – Discrete Mathematics.

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