Set Theory Calculator
Perform set operations including union, intersection, difference, complement, and more.
Define Sets
|A| = 5
|B| = 5
|U| = 10
Set Properties
A ⊆ B (A subset of B):No
B ⊆ A (B subset of A):No
A = B (Equal sets):No
Disjoint (A ∩ B = ∅):No
Set Operations
A ∪ B (Union):
{1, 2, 3, 4, 5, 6, 7}
A ∩ B (Intersection):
{3, 4, 5}
Differences
A - B (A minus B):
{1, 2}
B - A (B minus A):
{6, 7}
A Δ B (Symmetric Difference):
{1, 2, 6, 7}
Complements
A' (Complement of A):
{6, 7, 8, 9, 10}
B' (Complement of B):
{1, 2, 8, 9, 10}
Set Theory Formulas
Basic Operations
- Union: A ∪ B = {x : x ∈ A or x ∈ B}
- Intersection: A ∩ B = {x : x ∈ A and x ∈ B}
- Difference: A - B = {x : x ∈ A and x ∉ B}
- Complement: A' = {x : x ∈ U and x ∉ A}
Cardinality Formulas
- |A ∪ B| = |A| + |B| - |A ∩ B|
- |A - B| = |A| - |A ∩ B|
- |A Δ B| = |A| + |B| - 2|A ∩ B|