In: Advanced Math
Unless otherwise noted, all sets in this module are finite. Prove the following statements...
1. If A and B are sets then (a) |A ∪ B| = |A| + |B| − |A ∩ B| and (b) |A × B| = |A||B|.
2. If the function f : A→B is (a) injective then |A| ≤ |B|. (b) surjective then |A| ≥ |B|.
3. For each part below, there is a function f : R→R that is (a) injective and surjective. (b) injective but not surjective. (c) surjective but not injective. (d) neither injective nor surjective.