How do I prove a) and b)?

9. Let (X, all) and (Y,d2) be metric spaces and K C X compact. Let g : X a Y be a continuous functiOn. We will show that, for all a > 0, there exists a natural number M = M (a) E N such that tMMyWDS+MwwL for all as, y E K. We will prove the statement by way of contradiction. Prove the following. a) If the statement is not true, then there exist a positive number 50 > 0 and two sequences (In) and (yn) in K such that d2(g(wn)7 9%)) > 0 + ndl($m am). for all n E N. b) There exists a positive constant C such that, for all n E N, C 0 s dummy...) + 8\"