Mathematics Questions and Answers – Venn Diagrams

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This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Venn Diagrams”.

1. In the given Venn diagram, is set A subset of set B?
mathematics-questions-answers-venn-diagrams-q1
a) True
b) False
View Answer

Answer: b
Explanation: For set A to be the subset of B, whole set A must lie inside set B which is not so in given Venn diagram so, set A is not subset of set B.
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2. In the given Venn diagram, is set A subset of set U?
mathematics-questions-answers-venn-diagrams-q1
a) True
b) False
View Answer

Answer: a
Explanation: For set A to be the subset of U, whole set A must lie inside set U which is given in Venn diagram so, set A is subset of set U.

3. Which of the following statement is correct?
mathematics-questions-answers-venn-diagrams-q3
a) A is subset of B
b) B is subset of A
c) U is subset of A and B
d) A and B are subsets of U
View Answer

Answer: d
Explanation: Since set A and set B lie completely inside set U as given in diagram so they are subsets of set U and set U is superset of set A and B.
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4. If n(A)=10, n(B)=20, c=5 in the given Venn diagram. Find a and b.
mathematics-questions-answers-venn-diagrams-q4
a) a=10 and b=15
b) a=5 and b=15
c) a=15 and b=10
d) a=15 and b=5
View Answer

Answer: b
Explanation: From the given diagram, a + c = 10 => a+5=10 => a=5
and b + c = 20 => b+5=20 => b=15

5. In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like only tea?
mathematics-questions-answers-venn-diagrams-q5
a) 10
b) 20
c) 30
d) 40
View Answer

Answer: c
Explanation: Given, a + b + c + d = 100, a + c = 40, b + c = 30, c = 10
a+10=40 => a=30 i.e. 30 persons like only tea.
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6. In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like only coffee?
mathematics-questions-answers-venn-diagrams-q5
a) 10
b) 20
c) 30
d) 40
View Answer

Answer: b
Explanation: Given, a + b + c + d = 100, a + c = 40, b + c = 30, c = 10
b+10=30 => b=20 i.e. 20 persons like only coffee.

7. In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like either tea or coffee?
mathematics-questions-answers-venn-diagrams-q5
a) 20
b) 40
c) 50
d) 60
View Answer

Answer: d
Explanation: Given, a + b + c + d = 100, a + c = 40, b + c = 30, c = 10
b+10=30 => b=20
a + b + c = 40+20 = 60 i.e. 60 persons like either tea or coffee.
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8. In a population of 100 persons, 40 persons like tea and 30 persons like coffee. 10 persons like both of them. How many persons like neither tea nor coffee?
mathematics-questions-answers-venn-diagrams-q5
a) 20
b) 40
c) 50
d) 60
View Answer

Answer: b
Explanation: Given, a + b + c + d = 100, a + c = 40, b + c = 30, c = 10
b+10=30 => b=20
a + b + c = 40+20 = 60
d+60=100 => d=40 i.e. 40 persons like neither tea nor coffee.

9. Which of the following is correct?
mathematics-questions-answers-venn-diagrams-q9
a) A is subset of B
b) B is subset of A
c) U is subset of A and B
d) U is subset of A
View Answer

Answer: a
Explanation: In the given Venn diagram, A is completely inside B which is completely inside U. So, A is subset of B and both A and B are subset of U.
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10. Which of the following is set A?
mathematics-questions-answers-venn-diagrams-q10
a) {1,2,3,4,5}
b) {2,4}
c) {2,3,4}
d) {3}
View Answer

Answer: b
Explanation: Elements that lie inside the boundary of A are 2 and 4 so set A = {2,4}. Elements lying outside boundary of A are not part of A.

11. Which of the following is set B?
mathematics-questions-answers-venn-diagrams-q10
a) {1,2,3,4,5}
b) {2,4}
c) {2,3,4}
d) {3}
View Answer

Answer: c
Explanation: Elements that lie inside the boundary of B are 2, 3, 4 so set B = {2, 3, 4}. Elements lying outside boundary of B are not part of B.

12. Which of the following is set representing A but not B?
mathematics-questions-answers-venn-diagrams-q10
a) {1,2,3,4,5}
b) {2,4}
c) {2,3,4}
d) { }
View Answer

Answer: d
Explanation: Since A lie completely inside B so, A is a subset of B. All elements of A also belongs to B. Hence, there is no element that lie in A and not in B. Set is { }.

13. Which of the following is set representing B but not A?
mathematics-questions-answers-venn-diagrams-q10
a) { }
b) {2,4}
c) {2,3,4}
d) {3}
View Answer

Answer: d
Explanation: Element that lie inside the boundary of B but outside the boundary of A is 3. So, element that belongs to B but not A is 3. Set is {3}.

14. Which of the following is set representing neither A nor B?
mathematics-questions-answers-venn-diagrams-q10
a) {1,5}
b) {2,4}
c) {2,3,4}
d) { }
View Answer

Answer: a
Explanation: Elements that lie inside the boundary of U but outside the boundary of A and B are 1,5. So, elements that belong to neither A nor B are 1,5. Set is {1,5}.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter