Class 11 Maths Sets | Union on Sets |

**Union on Sets**

Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once. The symbol ‘∪’ is used to denote the union. Symbolically, we write A ∪ B and usually read as ‘A union B’.

A ∪ B = { x : x ∈A or x ∈B }

**Numerical**: Let A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}. Find A ∪ B.

**Solution** We have A ∪ B = { 2, 4, 6, 8, 10, 12}

Note: Common elements 6 and 8 have been taken only once while writing A ∪ B. In the Venn diagram below, area in the green represents A ∪ B

**Some Properties of the Operation of Union**

(i) A ∪ B = B ∪ A (Commutative law)

(ii) ( A ∪ B ) ∪ C = A ∪ ( B ∪ C) (Associative law )

(iii) A ∪ φ = A (Law of identity element, φ is the identity of ∪)

(iv) A ∪ A = A (Idempotent law)

(v) U ∪ A = U (Law of U)

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