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?

a) True

b) False

View Answer

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.

2. In the given Venn diagram, is set A subset of set U?

a) True

b) False

View Answer

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?

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

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.

4. If n(A)=10, n(B)=20, c=5 in the given Venn diagram. Find a and b.

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

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?

a) 10

b) 20

c) 30

d) 40

View Answer

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.

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?

a) 10

b) 20

c) 30

d) 40

View Answer

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?

a) 20

b) 40

c) 50

d) 60

View Answer

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.

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?

a) 20

b) 40

c) 50

d) 60

View Answer

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?

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

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.

10. Which of the following is set A?

a) {1,2,3,4,5}

b) {2,4}

c) {2,3,4}

d) {3}

View Answer

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?

a) {1,2,3,4,5}

b) {2,4}

c) {2,3,4}

d) {3}

View Answer

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?

a) {1,2,3,4,5}

b) {2,4}

c) {2,3,4}

d) { }

View Answer

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?

a) { }

b) {2,4}

c) {2,3,4}

d) {3}

View Answer

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?

a) {1,5}

b) {2,4}

c) {2,3,4}

d) { }

View Answer

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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