10. Let A, B and C be sets and let g : A - B and f : B - C be functions. a. In the following question, if your answer is yes, give a proof. If the answer is no, give a simple counter example. (a) If fog is one-to-one, does it follow that f is one-to-one? (b) If fog is one-to-one, does it follow that g is one-to-one? (c) If fog is onto, does it follow that fis onto? (d) If fog is onto, does it follow that g is onto? b. Show that if g : A - B and f : B - C are bijections, then the composite function fog : A - C is a bijection by showing that fog is one-to-one and that it is onto. One-to-one: Have to show that if a 1, a2 6 A and a, # a2, then (fog)(a1) # (fog)(a2). Onto: Have to show that (Vc e C) (3a E A) such that (fog) (a) = c