Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. If...

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.

Expert Solution

Colby Messinger answered 2 years ago

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Unless otherwise noted, all sets in this module are finite. Prove the following statements... 1. If...

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