) Let be an equivalence relation on a set A. Let F : A Y be a function such that F(a) = F(b) for all a,b such that a b. Let A/ be the set of equivalence classes of A, and let [a] denote the equivalence class which contains a. Prove that there is a unique function G : (A/ ) Y such that G([a]) = F(a) for all a A.