Question

If a set has 31 proper subsets, then the number of elements in the set is ______.

• A. 5

Answer 1

The correct option is A 5
If a set has 'n' elements, then the number of proper subsets, it has = $2^n-1$.

Given: A set has 31 proper subsets

$\therefore 2^n-1=31$
$\Rightarrow 2^n=32$
$\Rightarrow 2^n=2^5$

As bases are equal, so by comparing the exponents we get,
n= 5
$\therefore$ the number of elements in the set is 5.