In set theory, union (denoted as ∪) is a set operation between two sets that forms a set containing the elements of both sets.
Formally, union A ∪ B means that if a ∈ A ∪ B, then a ∈ A ∨ a ∈ B, where ∨ - is logical or. We see this connection between ∪ and ∨ symbols.
The union operation is:
The union of any finite number of sets may be defined inductively, as
The union of a general family of sets Xλ as λ ranges over a general index set Λ may be written in similar notation as
We may drop the indexing notation and define the union of a set to be the set of elements of the elements of that set:
In this notation the union of two sets A and B may be expressed as