How many subsets does the set F = {1, 2, 3, 4, 5} have?
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11 ANSWERS
Phil Scovis
Phil Scovis
Answered Oct 4, 2016
For each element, a subset either has, or does not have that element. Thus, the number of possibilities is 2n
2
n
, where n is the number of elements.
In this example, there are 5
5
elements, so there are 25=32
2
5
=
32
different subsets.
Here they are:
{}
{1}
{2}
{1,2}
{3}
{1,3}
{2,3}
{1,2,3}
{4}
{1,4}
{2,4}
{1,2,4}
{3,4}
{1,3,4}
{2,3,4}
{1,2,3,4}
{5}
{1,5}
{2,5}
{1,2,5}
{3,5}
{1,3,5}
{2,3,5}
{1,2,3,5}
{4,5}
{1,4,5}
{2,4,5}
{1,2,4,5}
{3,4,5}
{1,3,4,5}
{2,3,4,5}
{1,2,3,4,5}
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