Examples on Venn Diagram

Solved examples on Venn diagram are discussed here.

From the adjoining Venn diagram, find the following sets.

(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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