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
B
34
C
42
D
41

Solution

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