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
● Finite Sets and Infinite Sets
● Problems on Intersection of Sets
● Problems on Complement of a Set
● 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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