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Question

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


A
25
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B
34
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C
42
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D
41
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Solution

The correct option is D 41
Given, $$S=\left \{1, 2, 3, 4\right \}$$

Each element can be put in $$3$$ ways either in subsets or we don't put in any subset.

Total number of unordered pairs of disjoint subsets,
$$\displaystyle =\frac {3^n+1}{2}=\frac {3^4+1}{2}=41$$

Mathematics

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