**Definition of Union of Sets**

- Combining all the elements of any two sets is called the Union of those sets.
- Union of two sets A and B is obtained by combining all the members of the sets and is represented as
*A*∪*B*.

**More about Union of Sets**

- In the union of sets, element is written only once even if they exist in both the sets.
- Union of two sets is commutative i.e. if A and B are two sets, then
*A*∪*B*=*B*∪*A* - Union of sets is also associative. If A, B, and C are three sets, then
*A*∪ (*B*∪*C*) =*(A*∪*B*) ∪*C*

**Example of Union of Sets**

- If A = {1, 2, 3, 4, 5} and B = {2, 4, 6}, then the union of these sets is A ∪ B = {1, 2, 3, 4, 5, 6}.

This can also be represented by using Venn diagram as:

**Solved Example on Union of Sets**

A is the set of all odd numbers less than 10 and B, the set of all prime numbers less than 20. If C is the union of sets A and B, which of the following sets represent the set C?

Choices:

A. {3, 5, 7}

B. {1, 2, 3, 5, 7, 9, 11, 13, 17, 19}

C. {1, 2, 3, 5, 7, 9, 13}

D. {1, 2, 3, 7, 11, 13, 19}

Correct Answer: D

Solution:

Step 1:Set of all odd numbers less than 10 = {1, 3, 5, 7, 9}

Step 2:Set of all prime numbers less than 20 = {2, 3, 5, 7, 11, 13, 17, 19}

Step 3:Union of these two sets = {1, 3, 5, 7, 9} ∪ {2, 3, 5, 7, 11, 13, 17, 19}

Step 4:= {1, 2, 3, 5, 7, 9, 11, 13, 17, and 19}

Step 5:So, {1, 2, 3, 5, 7, 9, 11, 13, 17, and 19} is the union of the given two sets.

**Related Terms for Union of Sets**

- Complement of a Set
- Element
- Empty Set
- Intersection of Sets
- Member of a Set
- Number Sets
- Set