Hint: When trying to prove that one of the directions is correct, consider both a di- rect proof and a proof by contraposition. When trying to disprove, come up with a very simple counterexample where the cardinalities of the sets are no more than 2.

Let A,B, and C be finite sets and f:AB and g:Im(f)C be functions such that g is a bijection. Bob claims A=C if and only if f is an injection. For each direction ( and ),either prove or disprove the Bob's claim. Note: Im(f) denotes the image of f