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how to find total no of unordered pairs of

How to find total no. of unordered pairs of disjoint subsets of a finite set?

Solution) Suppose A and B are two such disjoint subsets of the set S. Then every element can go into A or B or the set S (3 choices). We only require to exclude the possibility of all elements choosing to be in S itself. Therefore the number of ways is 3ⁿ-1

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