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  • Let . The total number of unordered pairs of disjoint subsets of<img alt="S" src="http

Let S=\{1,2,3,4\}. The total number of unordered pairs of disjoint subsets ofSis equal to

Option: 1

25


Option: 2

34


Option: 3

42


Option: 4

41


Answers (1)

best_answer

Let A and B be two subsets of S. If \mathrm{x \in S}, then \mathrm{x } will not belong to \mathrm{A \cap B } if x belongs to at most one of A, B. Thus can happen in 3 ways.

Thus, there are \mathrm{3^{4}=81} subsets of \mathrm{S} for which \mathrm{A \cap B=\phi}.
Out of these there is just one way for which \mathrm{A=B=\phi}.

As we, are interested in unordered pairs of disjoint sets, the number of such subsets is

\frac{1}{2}\left(3^{4}-1\right)+1=41.

Posted by

Ajit Kumar Dubey

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