Question

Calculate the number of proper subsets of $A$, where set $A$ = {$x:x$ is a prime number, $x<19$}.

• A. 31
• B. 63
• C. 127
• D. 255

Answer 1

The correct option is C 127

Given that set $A$ = {$x:x$ is a prime number, $x<19$}, we get,

$A$ = {$2,3,5,7,11,13,17$}

Therefore, $n\left(A\right)$ = 7.

Number of proper subsets of a set = $2^n$ - 1, where $n$ is the number of elements

Hence, number of proper subsets of set $A$ = $2^7$ - 1
= $128-1$
= $127$