Power Set Calculator

Count the subsets (power set size) of a set with n elements.

Number of subsets 16

Proper subsets 15

Formula: |P(S)| = 2ⁿ

Step-by-step with your numbers:

1. Values used:

2. Number of elements = 4

4. Number of subsets = Number of elements squared = 4 x 4 = 16

5. Proper subsets = 15

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The power set is the set of all subsets, including the empty set and the set itself.

The math behind it

A set of n elements has 2ⁿ subsets, because each element is either in or out of a given subset. Proper subsets exclude the set itself, giving 2ⁿ − 1.

A set with 4 elements has 2⁴ = 16 subsets.

Is the empty set counted?

Yes — the empty set is a subset of every set.