Solved problems on complement of a set are given below to get a fair idea how to find the complement of two or more sets.
We know, when U be the universal set and A is a subset of U. Then the complement of A is the set all elements of U which are not the elements of A.
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Solved problems on complement of a set:
1. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4} and B = {2, 4, 6, 8}.
(i) Find A'
(ii) Find B'
Solution:
(i) A' = U - A
= {1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4}
= {5, 6, 7, 8, 9}
(ii) B' = U - B
= {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8}
= {1, 3, 5, 7, 9}
More worked-out problems on complement of a set.
2. Let A = {3, 5, 7}, B = {2, 3, 4, 6}
and C = {2, 3, 4, 5, 6, 7, 8}
(i) Verify (A ∩ B)' = A' ∪ B'
(ii) Verify (A ∪ B)' = A' ∩ B'
Solution:
(i) (A ∩ B)' = A' ∪ B'
L.H.S. = (A ∩ B)'
A ∩ B = {3}
(A ∩ B)' = {2, 4, 5, 6, 7, 8} ……………….. (1)
R.H.S. = A' ∪ B'
A’ = {5, 7, 8}
B’ = {2, 4, 6}
A’∪B’
= {2, 4, 5, 6, 7, 8} ……………….. (2)
From (1) and (2), we conclude that;
(A ∩ B)' = (A' ∪ B')
(ii) (A ∪ B)' = A' ∩ B'
L.H.S. = (A ∪ B)'
A∪B
= {2, 3, 4, 5, 6, 7}
(A ∪
B)' = {8} ……………….. (1)
R.H.S. = A' ∩ B'
A' = {2, 4, 6, 8}
B' = {5, 7, 8}
A' ∩ B' = {8} ……………….. (2)
From (1) and (2), we conclude that;
(A ∪ B)' = A' ∩ B'
● Set Theory
● Finite Sets and Infinite Sets
● Problems on Intersection of Sets
● Problems on Operation on Sets
● Venn Diagrams in Different Situations
● Relationship in Sets using Venn Diagram
● Union of Sets using Venn Diagram
● Intersection of Sets using Venn Diagram
● Disjoint of Sets using Venn Diagram
● Difference of Sets using Venn Diagram
8th Grade Math Practice
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