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)
Symbol for Union of a finite no. of sets:
Union of a finite number of sets is written as,
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