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Power Set Calculator
Generate all possible subsets of a given set
Maximum 6 elements. Separate with commas.
📐Power Set Properties
Definition
Set of all subsets of a set
Including empty set and the set itself
Size Formula
|P(S)| = 2^|S|
Where |S| is the number of elements
Empty Set
Always included in power set
∅ ∈ P(S) for any set S
Original Set
Always included in power set
S ∈ P(S) for any set S
💡Power Set Examples
P({}) = ?
{ ∅ }
Power set of empty set has 1 element
P({a}) = ?
{ ∅, {a} }
2 subsets: empty and original
P({a, b}) = ?
{ ∅, {a}, {b}, {a,b} }
4 subsets total
P({1, 2, 3}) = ?
8 subsets (2³)
Includes all combinations
💼Applications
Mathematics
• Set theory
• Combinatorics
• Topology
Computer Science
• Algorithm design
• Database queries
• Complexity analysis
Logic
• Boolean algebra
• Propositional logic
• Truth tables