﻿ Definition and examples union of sets | define union of sets - Algebra- Free Math Dictionary Online

# Union of Sets

## 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

### Examples 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

#### Ques: 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}

#### 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.

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