If p and q are two statements, which of the following equivalences hold? (A) ~(p ∧ q) ≡ ~p ∨ ~q (B) ~(p ∨ q) ≡ ~p ∧ ~q (C) p ∧ ~p ≡ T (D) ~(p ⇒ q) ≡ p ∧ ~q (E) p ∨ q ≡ ~p ∨ ~q

1. A(A), (B) and (D) only
2. B(A), (C) and (D) only
3. C(C), (D) and (E) only
4. D(A), (B) and (C) only

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Correct answer: A. (A), (B) and (D) only

Explanation

A and B are De Morgan's laws, and D holds because p ⇒ q is false only when p is true and q is false. p ∧ ~p is a contradiction (F, not T), and E is false.