(a) Show that if f : A → B is injective and E ⊂ A, then f-1( f (E)) = E. Give an example to show that equality need not hold if f is not injective.
(b) Show that if f : A → B is surjective and H ⊂ B, then (f-1(H)) = H. Give an example to show that equality need not hold if f is not surjective.