Mathematics Questions and Answers – Operation on Sets-2

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This set of Mathematics Quiz focuses on “Operation on Sets-2”.

1. If set A={1,2,3,4} and B={3,4,5,6}. Find A-B.
a) {1,2,3,4,5,6}
b) {3,4}
c) {1,2}
d) {5,6}
View Answer

Answer: c
Explanation: A-B is the set of elements that belongs to A but not to B. Here, 1 and 2 belongs to A but not to B. So,
A = {1,2,3,4}
B = {3,4,5,6}
A – B = {1,2,3,4} – {3,4,5,6} = {1,2}.
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2. If set A = {1,2,3,4} and B = {3,4,5,6}. Find B-A.
a) {1,2,3,4,5,6}
b) {3,4}
c) {1,2}
d) {5,6}
View Answer

Answer: d
Explanation: B-A is the set of elements that belongs to B but not to A. Here, 5 and 6 belongs to B but not to A. So,
A = {1,2,3,4}
B = {3,4,5,6}
B-A = {3,4,5,6} – {1,2,3,4} = {5,6}.

3. Does A-B=B-A always correct?
a) True
b) False
View Answer

Answer: b
Explanation: If A={1,2,3} and B={3,4,5}, then A-B={1,2,3} – {3,4,5} = {1,2} and B-A={3,4,5} – {1,2,3} = {4,5}. They are not equal so,
A-B and B-A are not always equal.
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4. If A-B=B-A then A and B are ____________
a) equivalent sets
b) equal sets
c) disjoint sets
d) empty sets
View Answer

Answer: b
Explanation: A-B is the set of elements that belongs to A but not to B and B-A is the set of elements that belongs to B but not to A. A-B=B-A is possible only when A and B are equal sets.

5. A – B, A ∩ B and B – A are mutually disjoint sets or not.
a) True
b) False
View Answer

Answer: a
Explanation: A – B, A ∩ B and B – A does not have any common region so the intersection of any two of them is null set. So, they are said to be mutually disjoint.

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6. If R is the set of real numbers and S is the set of rational numbers, then what is R – S?
a) Set of integers
b) Set of whole numbers
c) Set of irrational numbers
d) Set of complex numbers
View Answer

Answer: c
Explanation: There are two categories in real numbers which are rational and irrational. The real number which is not rational is irrational so, R-S denotes the set of irrational numbers.

7. A={1,2,3}, B={2,3,4}, C={2,3,5}, D={1,3,5,7}. Find (A∪B) ∩ (C∪D).
a) A
b) B
c) C
d) D
View Answer

Answer: a
Explanation: Here, A={1,2,3}, B={2,3,4}, C={2,3,5}, D={1,3,5,7}
A∪B={1,2,3}∪{2,3,4} = {1,2,3,4} and C∪D={2,3,5}∪{1,3,5,7} = {1,2,3,5,7}
(A∪B) ∩ (C∪D) = {1,2,3,4} ∩ {1,2,3,5,7} = {1,2,3} = A.
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8. A={1,2,3}, B={2,3,4}, C={2,3,5}, D={1,3,5,7}. Find (A∩B) ∪ (C∩D).
a) A
b) B
c) C
d) D
View Answer

Answer: c
Explanation: Here, A={1,2,3}, B={2,3,4}, C={2,3,5}, D={1,3,5,7}
A∩B = {1,2,3}∩{2,3,4} = {2,3} and C∩D = {2,3,5}∩{1,3,5,7} = {3,5}.
(A∩B) ∪ (C∩D) = {2,3} ∪ {3,5} = {2,3,5} = C.

9. If A is set of natural numbers, B is set of odd natural numbers and C is set of even natural numbers, then find A-B.
a) A
b) B
c) C
d) B-C
View Answer

Answer: c
Explanation: Natural number which is not odd is even. A-B means set of natural numbers excluding odd natural numbers so, A-B is set of even natural numbers Hence, A-B=C.
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10. If A is set of natural numbers, B is set of odd natural numbers and C is set of even natural numbers, then find B∪C.
a) A
b) B
c) C
d) B-C
View Answer

Answer: a
Explanation: Set which contains all odd natural numbers as well as all even natural numbers is set of natural numbers. So, B∪C=A.

11. If A is set of natural numbers, B is set of odd natural numbers and C is set of even natural numbers, then find B∩C.
a) A
b) B
c) C
d) Φ
View Answer

Answer: d
Explanation: Set of odd natural numbers and set of even natural numbers doesn’t have any common element as a natural number cannot be both odd and even. So, B∩C=Φ.

12. (A∪B) ∩ (B∪A) = __________
a) A
b) B
c) A∪B
d) A∩B
View Answer

Answer: c
Explanation: (A∪B) ∩ (B∪A) = (A∪B) ∩ (A∪B) (Commutative law)
= A∪B (A∩A=A).

13. (A∩B) ∪ (B∩A) = ______________
a) A
b) B
c) A∪B
d) A∩B
View Answer

Answer: d
Explanation: (A∩B) ∪ (B∩A) = (A∩B) ∪ (A∩B) (Commutative law)
= A∩B (A∪A=A).

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

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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