Considering α, β, γ as logical variables, which represent correct equivalences? (A) (α ∧ (β ∨ γ)) ≡ ((α ∧ β) ∨ (α ∧ γ)) (B) (α ∨ β) ≡ ¬α ∨ β (C) (α ⇒ β) ≡ (¬β ⇒ ¬α) (D) ¬(α ∨ β) ≡ (¬α ⇒ ¬β)

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

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Show answer & explanation

Correct answer: C. (A) and (C) only

Explanation

(A) is distributivity and (C) is the contrapositive. (B) is false (α ∨ β ≠ ¬α ∨ β), and ¬(α ∨ β) = ¬α ∧ ¬β, not ¬α ⇒ ¬β, so (D) is false.