How many subsets does a set have if the set has four elements?

Answer 1

16

Recall that every set is a subset of itself,

and the empty set is a subset of every set,

so

let {1, 2, 3, 4} be the original set.

Its subsets are:

{}

{1}

{2}

{3}

{4}

{1, 2}

{1, 3}

{1, 4}

{2, 3}

{2, 4}

{3, 4}

{1, 2, 3}

{1, 2, 4}

{1, 3, 4}

{2, 3, 4}

{1, 2, 3, 4}

* * * * *

A simpler rationale:

For any subset, each of the elements can either be in it or not. So, two choices per element. Therefore with 4 elements you have 2*2*2*2 or 24 choices and so 24 subsets.