Union of Sets
Related Words
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:
Video Examples: Intersection and union of sets
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}
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.
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