Let g: X -> Y and f: Y -> Z be functions. Justify your answer to each question below by giving either a proof or a counter example.

a) If f and f o g are one-to-one, does it follow that g is one-to-one?

b) If g and f o g are one-to-one, does it follow that f is one-to-one?

Any help would be much appreciated, thanks.