Power Set Calculator
Generate the power set (collection of all subsets) of any set.
Input Set
S = {a, b, c} (|S| = 3)
Power Set Statistics
|P(S)|
8
2^3
Proper Subsets
7
2^n - 1
Subsets by Size (Binomial Coefficients)
Size 0 (C(3,0)):1 subset
Size 1 (C(3,1)):3 subsets
Size 2 (C(3,2)):3 subsets
Size 3 (C(3,3)):1 subset
Power Set P(S)
The power set contains all 8 subsets of S
Size 0:
∅
Size 1:
{a}{b}{c}
Size 2:
{a, b}{a, c}{b, c}
Size 3:
{a, b, c}
All Subsets List
∅{a}{b}{c}{a, b}{a, c}{b, c}{a, b, c}
About Power Sets
Definition
The power set P(S) of a set S is the set of all subsets of S, including the empty set ∅ and S itself.
Properties
- |P(S)| = 2^|S| (always a power of 2)
- ∅ ∈ P(S) and S ∈ P(S) always
- The number of subsets of size k is C(n,k)