Question

If $\text{A}=\{x:x\text{is a prime number and}x<13\}$, then find the number of proper subsets of set $\text{A}$.​

• A. $32$
• B. $64$
• C. $31$
• D. $63$

Answer 1

The correct option is C $31$

$\text{A}=\{x:x\text{is a prime number and}$ $x<13\}$

$\text{A}=\{2,3,5,7,11\}$

Number of elements $=5$

Number of subsets $=2^n$, where $n$ is the number of elements. ​

Number of subsets $=2^5$​

Number of proper subsets $=2^n–1=2^5–1=32–1=31$​