Let f be a social welfare function satisfying the

Question

Let F be a social welfare function satisfying the independence of irrelevant alternatives property, and let a, b be two distinct alternatives. Let P N and QN be two strict preference profiles satisfying

a>_Pi b ⇔ a>Q_i b, ∀i ∈ N.

Prove that a ≈F(P N ) b if and only if a ≈F(QN ) b.