Question

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

• A. $41$
• B. $42$
• C. $25$
• D. $34$

Answer 1

The correct option is A $41$

Let $A\cap B=\varphi ,A,B\subset S$
The number of elements in $A:0$ Choices for $B:2^4$
The number of elements in $A:1$ Choices for $B:38$
The number of elements in $A:2$ Choices for $B:3$
Total number of possible subsets is $41$