The union of two sets is the set containing all elements from both sets.
The union of A and B, written A ∪ B, includes every element that belongs to A or B (or both). For example, if A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}. In probability, P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Union is a fundamental set operation alongside intersection and complement.
Set operations including union were formalized by Georg Cantor in the 1870s. The symbol ∪ was introduced by Giuseppe Peano in 1888. Union is one of the basic operations in Boolean algebra and is used in database queries (SQL UNION), logic, and probability theory.