# Operations on Sets - Union Set

#### description

• Some Properties of the Operation of Union

#### definition

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}

#### notes

If 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’.
Example- A= {0,1,2,3} and B= {0,2,4,5}
Solution- A ∪ B= {0,1,2,3,4,5}

Some Properties of the Operation of Union

a) Commutaive law-
The order of sequence to write the elements doesn't matter.
For instance, A ∪ B= B ∪ A

b) Associative law- If you perform opertions on three or more elements then it doesn't matter how you group them, you will end up with same set.
For instance, (A ∪ B)∪ C= A∪ (B ∪ C)

c) Law of identity element- If you combine anything with nothing then you get that anything as result. That means anything union with a null set will result in that anything.
For instance, A ∪ Ø= A

d) Idempotent law- if we take union of two same elements then result will be that single element because we are not taking anything new.
A ∪ A= A

e) Law of U- When a Universal set is combined with a subset then we get Universal set.
U ∪ A = A

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