Solution to Let C={A1, A2, ..., An} be a collection of finite sets that are pairwise disjoint. … - Sikademy
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Archangel Macsika

Let C={A1, A2, ..., An} be a collection of finite sets that are pairwise disjoint. Further suppose that |Ai|=i. Compute |U(i=1 to n)Ai|, and write your answer in the simplest closed form possible.

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,An},Ai=ii=1nAi=A1A2An=A1+A2++AnSince they are disjoint=1+2++n=i=1ni=2n(n+1)


Hence, \left| \bigcup_{i=1}^nA_i\right|=\frac{n(n+1)}{2}.

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