The **union of two** sets A and B is the set C which consists of all those elements which are either in A or in B (including those which are in both). In symbols, we write.

A ∪ B = { x : x ∈A or x ∈B }

**Venn diagram of Union**

## Some Properties of the Operation of Union

- A ∪ B = B ∪ A
**(Commutative law)** - ( A ∪ B ) ∪ C = A ∪ ( B ∪ C)
**(Associative law )** - A ∪ φ = A
**(Law of identity element, φ is the identity of ∪)** - A ∪ A = A
**(Idempotent law)** - U ∪ A = U
**(Law of U)**

**Example of Union in set**

**Example **Let A = { a, e, i, o, u } and B = { a, i, u }. Show that A ∪ B = A

**Solution **We have, A ∪ B = { a, e, i, o, u } = A.

This example illustrates that union of sets A and its subset B is the set A

itself, i.e., if B ⊂ A, then A ∪ B = A