Question

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

• A. 25
• B. 34
• C. 42
• D. 41

Answer 1

The correct option is D 41

Given, $S=\{1,2,3,4\}$

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,
$=\frac{3^n+1}{2}=\frac{3^4+1}{2}=41$