Subset Calculator
Check subset relationships between sets and enumerate all subsets.
Define Sets
A = {1, 2, 3} (|A| = 3)
B = {1, 2, 3, 4, 5} (|B| = 5)
Element Analysis
In A but not B:∅
In B but not A:{4, 5}
In both A and B:{1, 2, 3}
Subset Relationships
A ⊆ B (A is subset of B)TRUE
A ⊂ B (A is proper subset of B)TRUE
B ⊆ A (B is subset of A)FALSE
A = B (Sets are equal)FALSE
Subsets of A
8
2^3 = 8
Subsets of B
32
2^5 = 32
All Subsets of A
∅{1}{2}{1, 2}{3}{1, 3}{2, 3}{1, 2, 3}
Subset Definitions
Subset (⊆)
A ⊆ B means every element in A is also in B. A can equal B.
Proper Subset (⊂)
A ⊂ B means A ⊆ B and A ≠ B. B has at least one element not in A.
Number of Subsets
A set with n elements has 2^n subsets, including ∅ and itself.