9. Let f : A -+ B and 9 : B -+ C and define go f : A -+ C by (g 0 f)(x) := g(f(x)).

(a) Show that if f,g are 1-1 (respectively, onto), then go f is 1-1 (respectively, onto).

(b) [PIGEONHOLE PRINCIPLE] Prove that if f is 1-1 from A into B, then r 1 is 1-1 from f(A) onto A.

(c) Suppose that g is 1-1 from B onto C. Prove that f is I-Ion A (respectively, onto B) if and only if g 0 f is I-Ion A (respectively, onto C).