Subset Calculator
Use the subset calculator to generate the list of subsets of a given set or to determine how many subsets it has.
A ∪ B (union){1, 2, 3, 4, 5}5 elements
A ∩ B (intersection){3, 4}2 elements
A \ B (in A only){1, 2}
B \ A (in B only){5}
Symmetric difference{1, 2, 5}
A ⊆ B?NoA is a subset of B when nothing is in A alone
Disjoint?No
Power set of A
| Subsets | 2^4 = 16 subsets |
| Listed | ∅, {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} |
The method
union, intersection, difference and the power set
Counting subsets
A set with n elements has exactly 2ⁿ subsets, because each element is independently either in or out. That includes the empty set and the whole set — both are legitimate subsets.
Note the distinction between a subset (⊆, may equal the set) and a proper subset (⊂, must be strictly smaller). A set with n elements has 2ⁿ − 1 proper subsets.