Problems on Complement of a Set

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.

Click Here to know more about the complement of a set.

 

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

Sets Theory

Representation of a Set

Types of Sets

Finite Sets and Infinite Sets

Power Set

Problems on Union of Sets

Problems on Intersection of Sets

Difference of two Sets

Complement of a Set

Problems on Operation on Sets

Word Problems 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

Examples on Venn Diagram







8th Grade Math Practice

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