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:

Video Examples: Intersection and union of sets


    Example on UUnion 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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