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 AB.

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 AB = BA
  • Union of sets is also associative. If A, B, and C are three sets, then A ∪ (BC) = (AB) ∪ 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