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

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}.

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

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

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.

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

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

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.

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

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

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.

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

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

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.

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

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

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

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

Explanation: (A∩B) ∪ (B∩A) = (A∩B) ∪ (A∩B) (Commutative law)

= A∩B (A∪A=A).

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