Match List I with List II (logically equivalent expressions)
| List I | List II |
|---|---|
| (a) P ∧ (P → Q) | (I) P ∨ Q |
| (b) ¬(P ∨ Q) → (P ∧ Q) | (II) (P ∧ ¬P) ∨ (P ∧ Q) |
| (c) P → Q | (III) (¬P) ∨ Q |
| (d) P ∨ (Q ∧ R) | (IV) (P ∧ P) ∨ (P ∧ Q) ∨ (P ∧ R) ∨ (Q ∧ R) |
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Show answer & explanation
Correct answer: B. (a)-(II), (b)-(I), (c)-(III), (d)-(IV)
Explanation
P ∧ (P → Q) ≡ P ∧ Q ≡ (P ∧ ¬P) ∨ (P ∧ Q) (a-II). ¬(P ∨ Q) → (P ∧ Q) ≡ (P ∨ Q) ∨ (P ∧ Q) ≡ P ∨ Q (b-I). P → Q ≡ ¬P ∨ Q (c-III). The remaining pair is d-IV.More Discrete Structures and Optimisation questions
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