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

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Solution

The correct option is D
5

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

$∴ 2^{n} - 1 = 31$

$2^{n} = 32$

$2^{n} = 2^{5}$

As bases are equal, exponents may be equated

n= 5

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

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