Suppose that g is a function from A to B and f is a function from B to C. Show that:
a If f ◦ g is onto, then f must also be onto.
b If f ◦ g is one-to-one, then g must also be one-to-one.
c If f ◦ g is a bijection, then g is onto if and only if f is one-to-one.
(A, B, and C are sets)