# Class 11 Maths MCQ – Complement of a Set

This set of Class 11 Maths Chapter 1 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

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

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

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}

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}

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}.
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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}

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

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’

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

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

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.

Sanfoundry Global Education & Learning Series – Mathematics – Class 11.

To practice all chapters and topics of class 11 Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.