Let A and B be sets.

(a) Suppose f:AB and g:BA such that fog= id B

(g is right inverse for f and f is let inverse for g). Show that f is a surjection from A to B and g is an injection from B to A

(b) Suppose f is a surjection from A to B. Show that there exists a function g: BA such that fog = id B

(for this part, let Ay=f^-1[{y}] for all y in B. Show that Ay for all y in B)