Let g be a function from X to Y and let f be a function from
Y to Z. For each statement below, if the statement is true, prove it; otherwise,
give a counterexample.
i. If g is one-to-one, then f ◦ g is one-to-one.
ii. If g is onto, then f ◦ g is onto.
iii. If f is onto, then f ◦ g is onto.
iv. If f ◦ g is one-to-one, then f is one-to-one.