The union of two sets is another set made by including all the unique elements of the two given sets. In other words, in the union of two sets the common elements in the two sets are included only once. The symbol ‘∪’ is used to denote the union of sets. If A and B are two sets then the union of set A and set B is denoted by A∪B and it is read as ‘A union B’. Union of two sets A and B can be represented using a Venn diagram as shown below.
For example: say you need to find the union of the two sets A = {1, 3, 4, 6} and B = {2, 4, 6}.
A∪B = {1, 2, 3, 4, 6}. Even though both the sets contain the elements 4 and 6, they are included only once in the union.
Properties of union of sets
- A∪B = B∪A (Commutative law)
- A∪( B∪C) = (A∪B)∪C (Associative law)
- A∪ Ø = A (Identity law)
- A∪A = A (Idempotent law)
- U∪A = U (Law of universal set)