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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:

General unions

Finite unions

The union of any finite number of sets may be defined inductively, as

Infinite unions

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

See also