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

Dear Students,

Total disjoint subsets are 2^n-1 where n is the no of elements in the set.

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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 need to exclude the possibility of all elements choosing to be in S itself. Hence the number of ways is 3ⁿ-1

If there are pairs of unordered disjoint sets could be found, 3 is to the power n-1/2+1. This formula mostly asked in IIT and competitive questions.

Total subsets=( 3^n)+1So total unordered subsets will be half of it ....=(( 3^n )+1)/2Where n is the total no of discreet elements given in the finite set