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∣=i∣⋃i=1nAi∣=∣A1⋃A2⋃⋯⋃An∣=∣A1∣+∣A2∣+⋯+∣An∣Since they are disjoint=1+2+⋯+n=∑i=1ni=2n(n+1)
Hence,