Question

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

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

The correct option is B

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 (b)