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

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Advance 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 norsurjective.

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