In the field of computation theory, union is one of the regular operations. If A and B are languages (not necessarily regular languages) then the union of A and B (usually written A ∪ B) is defined as follows.
{x
| x ∈ A or x ∈ B}
In plain English: A ∪ B is the set of all strings which are either members of A or B or both.
For example, if A = {a,b,c}, and B = {c,d,e}
A ∪ B = {a,b,c,d,e}
Some interesting things to note about the union operation:
- The union of a set with any subset is equal to the original set (iff B ⊆ A, then A ∪ B = A).
- Regular languages are closed under the union operation. This means that if A and B are regular languages, then so is A ∪ B.