The power set P(S) of set S is the set of all subsets of S, including ∅ and S itself. If |S| = n, then |P(S)| = 2ⁿ. For S = {a,b,c}: P(S) = {∅, {a}, {b}, {c}, {a,b}, {a,c}, {b,c}, {a,b,c}}. The number of subsets of size k is C(n,k).
How to Use
Enter set elements:
- Input: Comma-separated
- Output: All subsets listed
- Grouped: By cardinality
Counting
- Total subsets: 2ⁿ
- Size-k subsets: C(n,k)
- Sum of C(n,k) for all k = 2ⁿ
Applications
Probability sample spaces, Boolean function inputs, database query optimization, logic circuit design, machine learning feature selection.
Step-by-Step Instructions
- 1Enter set elements.
- 2View all subsets.
- 3Check count by cardinality.
- 4Verify 2ⁿ total.
- 5Explore patterns.