Mathematics Questions and Answers – Complement of a Set

«
»

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

Answer: d
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.
advertisement

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

Answer: c
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

Answer: 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= U∩A’.
(A’)’ = (U∩A’)’ = U’∪A = A.
advertisement
advertisement

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

Answer: a
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

Answer: c
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}.
advertisement

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

Answer: c
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

Answer: a
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)’.
advertisement

8. Which of the following is equal to A∪A’?
a) U
b) A
c) A’
d) U’
View Answer

Answer: a
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

Answer: c
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.
advertisement

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

Answer: c
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 areas of Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

advertisement
advertisement
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