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Prove the following statements! 1. If A and B are sets then (a) |A ∪ B| =...

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Advance Math

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

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