Question

If $S$ is a set then $|S|$ denotes number of elements in $S$. Let $S=\{1,2,3,4,5,6\}$. Number of different non-empty subsets $T$ of $S$ which do not contain $|T|$, is

• A. 30
• B. 31
• C. 32
• D. none

Answer 1

Answer: (B)

Single element subset which do not contain 1 is ${}^5{C}_1$.
$\therefore {}^5{C}_1+{}^5{C}_2+{}^5{C}_3+{}^5{C}_4+{}^5{C}_5=2^5-1=31$