Which of the following pairs of propositions are not logically equivalent?

1. A((p → r) ∧ (q → r)) and ((p ∨ q) → r)
2. Bp ↔ q and (¬p ↔ ¬q)
3. C((p ∧ q) ∨ (¬p ∧ ¬q)) and p ↔ q
4. D((p ∧ q) → r) and ((p → r) ∧ (q → r))

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: D. ((p ∧ q) → r) and ((p → r) ∧ (q → r))

Explanation

(p → r) ∧ (q → r) ≡ (p ∨ q) → r, not (p ∧ q) → r: with p true, q false, r false the first is true and the second false. A, B and C are genuine equivalences.