Question

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

• A. 4
• B. 6
• C. 7
• D. 5

Answer 1

The correct option is D

5

If a set has 'n' elements the number of proper subsets is $2^n-1$.

$\therefore 2^n-1=31$

$2^n=32$

$2^n=2^5$

As bases are equal, exponents may be equated

n= 5

Hence,the number of elements in the set is 5.