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We denote |S| the number of elements of a set S. (1) Let A and B...

We denote |S| the number of elements of a set S. (1) Let A and B be two finite sets. Show that if A ∩ B = ∅ then A ∪ B is finite and |A ∪ B| = |A| + |B| . Hint: Given two bijections f : A → N|A| and g : B → N|B| , you may consider for instance the function h : A ∪ B → N|A|+|B| defined as h (a) = f (a) if a ∈ A g (a) + |A| if a ∈ B. (2) Let A and B be two finite sets (not necessarily disjoint). Show that A ∪ B is finite. Hint: It may be useful to show that A∪B = A∪(B\A) and A∩(B\A) = ∅.

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