∪∩
Union & Intersection Calculator
Calculate set union, intersection, and differences
Set Operation
📐Set Operation Definitions
Union (A ∪ B)
All elements in A or B (or both)
{x : x ∈ A or x ∈ B}
Intersection (A ∩ B)
Elements in both A and B
{x : x ∈ A and x ∈ B}
Difference (A \ B)
Elements in A but not in B
{x : x ∈ A and x ∉ B}
Symmetric Difference (A △ B)
Elements in A or B but not both
(A \ B) ∪ (B \ A)
💡Examples
A = {1, 2, 3}, B = {3, 4, 5}
A ∪ B = {1, 2, 3, 4, 5}
A ∩ B = {3}
A = {1, 2, 3}, B = {3, 4, 5}
A \ B = {1, 2}
A △ B = {1, 2, 4, 5}
A = {a, b}, B = {c, d}
A ∪ B = {a, b, c, d}
A ∩ B = ∅
A = {1, 2}, B = {1, 2}
A ∪ B = {1, 2}
A ∩ B = {1, 2}
🔢Set Operation Properties
Commutative
A ∪ B = B ∪ A
A ∩ B = B ∩ A
Associative
(A ∪ B) ∪ C = A ∪ (B ∪ C)
(A ∩ B) ∩ C = A ∩ (B ∩ C)
Distributive
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
Identity
A ∪ ∅ = A
A ∩ U = A (U = universal set)
💼Applications
Computer Science
• Database queries
• Set operations
• Data filtering
Statistics
• Sample spaces
• Event combinations
• Venn diagrams
Logic
• Boolean operations
• Set theory
• Category theory