5. a.) Prove the following directly from the axiom of choice: For any function f from a set X to itself there exists g: X - X with fof = f. b.) Prove the converse of Exercise 5. In detail: Suppose that for any set X and any function f: X - X there exists g: X - X with fgf = f. Prove that any set has a choice function. (Hint: Use the version AC'.)