Examples on Venn Diagram

Solved examples on Venn diagram are discussed here.

From the adjoining Venn diagram, find the following sets.

Examples on Venn Diagram

(i) A

(ii) B 

(iii) ξ 

(iv) A'

(v) B'

(vi) C'

(vii) C - A 

(viii) B - C 

(ix) A - B 

(x) A ∪ B 

(xi) B ∪ C 

(xii) A ∩ C 

(xiii) B ∩ C

(xiv) (B ∪ C)'

(xv) (A ∩ B)'

(xvi) (A ∪ B) ∩ C

(xvii) A ∩ (B ∩ C) 

Answers for examples on Venn diagram are given below:

(i) A

= {1, 3, 4, 5}


(ii) B

= {4, 5, 6, 2}


(iii) ξ

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}


(iv) A'

= {2, 6, 7, 8, 9, 10}     all elements of universal set leaving the elements of set A.


(v) B'

= {1, 3, 7, 8, 9, 10}     all elements of universal set leaving the elements of set B.


(vi) C’ = To find

C = {1, 5, 6, 7, 10}

Therefore, C' = {2, 3, 4, 8, 9}     all elements of universal set leaving the elements of set C.


(vii) C - A

Here C = {1, 5, 6, 7, 10}

A = {1, 3, 4, 5}

then C – A = {6, 7, 10}     excluding all elements of A from C.


(viii) B - C

Here B = {4, 5, 6, 2}

C = {1, 5, 6, 7, 10}

B - C = {4, 2}     excluding all elements of C from B.


(ix) B - A

Here B = {4, 5, 2} 

A = {1, 3, 4, 5} 

B - A = {6, 2}     excluding all elements of A from C. 


(x) A ∪ B 

Here A = {1, 3, 4, 5} 

B = (4, 5, 6, 2} 

A ∪ B = {1, 2, 3, 4, 5, 6} 


(xi) B ∪ C

Here B = {4, 5, 6, 2}

C = {1, 5, 6, 7, 10}

B ∪ C = {1, 2, 4, 5, 6, 7, 10}


(xii) (B ∪ C)'

Since, B ∪ C = {1, 2, 4, 5, 6, 7, 10}

Therefore, (B ∪ C)' = {3, 8, 9} 


(xiii) (A ∩ B)' 

A = {1, 3, 4, 5} 

B = {4, 5, 6, 2}

(A ∩ B) = {4, 5} 

(A ∩ B)' = {1, 2, 3, 6, 7, 8, 9, 10} 


(xiv) (A ∪ B) ∩ C

A = {1, 2, 3, 4} 

B = {4, 5, 6, 2} 

C = {1, 5, 6, 7, 10} 

A ∪ B= {1, 2, 3, 4, 5, 6}

(A ∪ B) ∩ C = {1, 5, 6} 


(xv) A ∩ (B ∩ C) 

A = {1, 3, 4, 5}

B = {4, 5, 6, 2} 

C = {1, 5, 6, 7, 10} 

B ∩ C = {5, 6} 

A ∩ (B ∩ C) = {5}

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 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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