[Discrete Math] f: A-->B; surjective? find necessary & sufficient condition. Ok in practice for my discrete exam, I have the following problem. Let f : A->B be a function. a) Show that if f is surjective, then whenever g o f = h o f holds for the functions g,h : B -> C, then g =h. b) Find a necessary and sufficient condition for f such that for any set C and any functions g,h:B->C, if g o f = h o f, then g = h I need help at starting this problem. How do I start on a)? Here's what I know, g o f : A -> C , so (g o f)(a) = g(f(a)), such that (a,c) are elements in g o f <=> [tex]\exists b \in B:(a,b)\in f[/tex], [tex](b,c)\in g[/tex] I hope that latex stuff comes out right. Anyways I've got 3 hours to figure this out. I just need a push forward, maybe some hints, or suggestions.