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

$41$

Explanation for the correct option

Finding the number of unordered pairs of a disjoint subset

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

The formula for unordered pairs of disjoint subsets is,

$\left[\frac{3^n+1}{2}\right]$

and here $S$ has four elements. Hence, $n=4$

Putting $n=4$ in the formula we get,

$$\begin{gathered} =\frac{[3^4+1]}{2} \\ =\frac{82}{2} \\ =41 \end{gathered}$$

Therefore, the correct option is D.