#### 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