This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Complement of a Set”.

1. What does A’ denotes when U is a universal set?

a) A

b) Φ

c) U

d) U-A

View Answer

Explanation: Complement of a set A is a set that contains elements of U which are not the elements of A. So, A’=U-A.

2. If A= {2,3,5} and U be the set of prime factors of 210 then find A’.

a) {2,3,5}

b) {2,3,5,7}

c) {7}

d) Φ

View Answer

Explanation: 210=2*3*5*7 => U = {2,3,5,7}.

Complement of a set A is a set which contains elements of U which are not the elements of A. So, A’=U-A={2,3,5,7} – {2,3,5} = {7}.

3. Is (A’)’=A?

a) True

b) False

View Answer

Explanation: Complement of a set A is a set that contains elements of U which are not the elements of A. So, A’=U-A= U∩A’.

(A’)’ = (U∩A’)’ = U’∪A = A.

4. Let U = {1, 2, 3, 4, 5, 6}, A = {1,4} and B = {2,3,5}. Find A’.

a) {2,3,5,6}

b) {1,2,3}

c) {1,4,6}

d) {1,2,3,4,5,6}

View Answer

Explanation: Complement of a set A is a set which contains elements of U which are not the elements of A. So, A’ = U – A = {1, 2, 3, 4, 5, 6} – {1,4} = {2,3,5,6}.

5. Let U = {1, 2, 3, 4, 5, 6}, A = {1,4} and B = {2,3,5}. Find B’.

a) {2,3,5,6}

b) {1,2,3}

c) {1,4,6}

d) {1,2,3,4,5,6}

View Answer

Explanation: Complement of a set A is a set which contains elements of U which are not the elements of B. So, B’ = U – B = {1, 2, 3, 4, 5, 6} – {2,3,5} = {1,4,6}.

6. Let U = {1, 2, 3, 4, 5, 6}, A = {1,4} and B = {2,3,5}. Find A’∩B’.

a) {2,3,5,6}

b) {1,2,3}

c) {6}

d) {1,2,3,4,5,6}

View Answer

Explanation: Complement of a set A is a set which contains elements of U which are not the elements of A. A’ = U-A = {1, 2, 3, 4, 5, 6} – {1,4} = {2,3,5,6} and B’ = U-B = {1, 2, 3, 4, 5, 6} – {2,3,5} = {1,4,6}. A’∩B’={2,3,5,6} ∩ {1,4,6} = {6}.

7. Let U = {1, 2, 3, 4, 5, 6}, A = {1,4} and B = {2,3,5}. Then A’∩B’ is equal to (A∪B)’.

a) True

b) False

View Answer

Explanation: Complement of a set A is a set which contains elements of U which are not the elements of A. A’ = U-A = {1, 2, 3, 4, 5, 6} – {1,4} = {2,3,5,6} and B’ = U-B = {1, 2, 3, 4, 5, 6} – {2,3,5} = {1,4,6}. A’∩B’= {2,3,5,6} ∩ {1,4,6} = {6}.

A∪B = {1,2,3,4,5} => (A∪B)’={6}.

Hence, A’∩B’=(A∪B)’.

8. Which of the following is equal to A∪A’?

a) U

b) A

c) A’

d) U’

View Answer

Explanation: In the Venn diagram, region a denotes A and region b denotes A’. Region a and b together form universal set so, A∪A’=U.

9. If A is set of equilateral triangles then A’ is ________

a) set of isosceles triangles

b) set of scalene triangles

c) union of sets of scalene and isosceles triangles

d) intersection of sets of scalene and isosceles triangles

View Answer

Explanation: A is set of equilateral triangles i.e. triangles with all three sides equal.

Therefore, A’ is set of triangles with at least one side different i.e. may be all sides different or two sides equal so, A’ is union of sets of scalene and isosceles triangles.

10. Which of the following is not equal to set A?

a) A∩U

b) A∩Φ’

c) A∪A’

d) A∪Φ

View Answer

Explanation: In the Venn diagram, A∩U=> region common to A and U is a i.e. A

A∩Φ’ = A∩U = A (Φ’=U)

A∪A’=>region a and region b => U

A∪Φ=A.

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