# Union of Sets

Definition of Union of Sets:

Union of two given sets is the smallest set which contains all the elements of both the sets.

To find the union of two given sets A and B is a set which consists of all the elements of A and all the elements of B such that no element is repeated.

The symbol for denoting union of sets is ‘’.

For example;

Let set A = {2, 4, 5, 6}
and set B = {4, 6, 7, 8}

Taking every element of both the sets A and B, without repeating any element, we get a new set = {2, 4, 5, 6, 7, 8}

This new set contains all the elements of set A and all the elements of set B with no repetition of elements and is named as union of set A and B.

The symbol used for the union of two sets is ‘’.

Therefore, symbolically, we write union of the two sets A and B is A ∪ B which means A union B.

Therefore, A ∪ B = {x : x ∈ A or x ∈ B}

Solved examples to find union of two given sets:

1. If = {1, 3, 7, 5} and B = {3, 7, 8, 9}. Find union of two set A and B.

Solution:

A ∪ B = {1, 3, 5, 7, 8, 9}
No element is repeated in the union of two sets. The common elements 3, 7 are taken only once.

2. Let X = {a, e, i, o, u} and Y = {ф}. Find union of two given sets X and Y.

Solution:

X ∪ Y = {a, e, i, o, u}

Therefore, union of any set with an empty set is the set itself.

3. If set P = {2, 3, 4, 5, 6, 7}, set Q = {0, 3, 6, 9, 12} and set R = {2, 4, 6, 8}.

(i) Find the union of sets P and Q

(ii) Find the union of two set P and R

(iii) Find the union of the given sets Q and R

Solution:

(i) Union of sets P and Q is P ∪ Q

The smallest set which contains all the elements of set P and all the elements of set Q is {0, 2, 3, 4, 5, 6, 7, 9, 12}.

(ii) Union of two set P and R is P ∪ R

The smallest set which contains all the elements of set P and all the elements of set R is {2, 3, 4, 5, 6, 7, 8}.

(iii) Union of the given sets Q and R is Q ∪ R

The smallest set which contains all the elements of set Q and all the elements of set R is {0, 2, 3, 4, 6, 8, 9, 12}.

Notes:

A and B are the subsets of A ∪ B

The union of sets is commutative, i.e., A ∪ B = B ∪ A.

The operations are performed when the sets are expressed in roster form.

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, is the identity of )

(iv) A∪A = A                        (Idempotent law)

(v) U∪A = U                        (Law of ) ∪ is the universal set.

Notes:

A ∪ ϕ = ϕ ∪ A = A i.e. union of any set with the empty set is always the set itself.

Set Theory

Sets

Objects Form a Set

Elements of a Set

Properties of Sets

Representation of a Set

Different Notations in Sets

Standard Sets of Numbers

Types of Sets

Pairs of Sets

Subset

Subsets of a Given Set

Operations on Sets

Intersection of Sets

Difference of two Sets

Complement of a Set

Cardinal number of a set

Cardinal Properties of Sets

Venn Diagrams

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles 1. ### 2nd grade math Worksheets | Free Math Worksheets | By Grade and Topic

Dec 06, 23 01:23 AM

2nd grade math worksheets is carefully planned and thoughtfully presented on mathematics for the students.

2. ### Rupees and Paise | Paise Coins | Rupee Coins | Rupee Notes

Dec 04, 23 02:14 PM

Money consists of rupees and paise; we require money to purchase things. 100 paise make one rupee. List of paise and rupees in the shape of coins and notes: