Match List I with List II: match the logically equivalent propositions
| List I | List II |
|---|---|
| A. p → q | I. (p ∧ q) ∨ (¬p ∧ ¬q) |
| B. ¬(p ∨ (¬p ∧ q)) | II. ¬p ∨ q |
| C. p ↔ q | III. ¬(p ∨ q) |
| D. ¬(p ↔ q) | IV. ¬p ↔ q |
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Show answer & explanation
Correct answer: C. A-II, B-III, C-I, D-IV
Explanation
p → q ≡ ¬p ∨ q (A-II). ¬(p ∨ (¬p ∧ q)) = ¬(p ∨ q) by absorption (B-III). p ↔ q ≡ (p ∧ q) ∨ (¬p ∧ ¬q) (C-I). ¬(p ↔ q) ≡ ¬p ↔ q (D-IV).More Discrete Structures and Optimization questions
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