Match the logically equivalent propositions. List I: A. p → q, B. ¬(p ∨ (¬p ∧ q)), C. p ↔ q, D. ¬(p ↔ q). List II: I. (p ∧ q) ∨ (¬p ∧ ¬q), II. ¬p ∨ q, III. ¬(p ∨ q), IV. ¬p ↔ q.

1. AA-I, B-III, C-II, D-IV
2. BA-I, B-II, C-III, D-IV
3. CA-II, B-III, C-I, D-IV
4. DA-II, B-III, C-IV, D-I

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Show answer & explanation

Correct answer: C. A-II, B-III, C-I, D-IV

Explanation

p → q ≡ ¬p ∨ q. p ∨ (¬p ∧ q) ≡ p ∨ q, so its negation is ¬(p ∨ q). p ↔ q is true when both are true or both false. ¬(p ↔ q) ≡ ¬p ↔ q.