Let . Let A0 ⊂ A and B0  ⊂ B.(a) Show that A0 ⊂ f−1 (f(A0)) and that equality holds if f i...

Let . Let A0 ⊂ A and B0  ⊂ B.

(a) Show that A0 ⊂ f−1 (f(A0)) and that equality holds if f is injective.

(b) Show that f(f−1(B0)) ⊂ B0 and that equality holds if f is surjective.