This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Subsets – 1”.

1. If every element of set X is in set Y then_____________

a) X⊂Y

b) Y⊂X

c) X=Y

d) X≠Y

View Answer

Explanation: If every element of set X is in set Y then X is called subset of Y. X⊂Y.

But every element of Y may or may not be the element of X so we can’t say Y⊂X and hence we can’t decide equality.

2. If set A is equal to set B then ____________

a) A⊂B

b) B⊂A

c) A⊂B and B⊂A

d) neither A⊂B nor B⊂A

View Answer

Explanation: If set A is equal to set B then every element of set A is in set B i.e. A⊂B and every element of set B is in set A i.e. B⊂A. Hence A⊂B and B⊂A.

3. Let X= {1,2,3}, Y= {}, Z= {1,2,3}, then which of the following is true?

a) X⊂Y

b) Only Y⊂X and Y⊂Z

c) Z⊂Y

d) Y⊂X and Y⊂Z and X⊂Z

View Answer

Explanation: Null set is the subset of every set so Y⊂X and Y⊂Z.

Since set X is equal to set Z so, Z⊂X and X⊂Z.

4. Let A= {2,3,5} and B= {3,5,7}. Which of the following is true?

a) A⊂B

b) B⊂A

c) A=B

d) A⊂A

View Answer

Explanation: Since every set is subset of itself so A⊂A and B⊂B.

Since every element of set A is not in set B so, A is not a subset of B. Also, every element of set B is not in set A so, B is not a subset of A. Hence, A≠B.

5. Let X be set of rational numbers. Which of the following is superset of X?

a) Set of real numbers

b) Set of natural numbers

c) Set of whole numbers

d) Set of integers

View Answer

Explanation: If X is subset of Y then Y is called superset of X. Set of rational numbers is subset of set of real numbers so, set of real numbers is called superset of X.

6. Let X be set of rational numbers. Which of the following is not subset of X?

a) Set of real numbers

b) Set of natural numbers

c) Set of whole numbers

d) Set of integers

View Answer

Explanation: Set of rational numbers { x : x=p/q where p and q are integers and q≠0}.

Set of real number is not a subset of X. Set of natural numbers, whole numbers, integers are subset of X.

7. Let A = {1, 3}, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}. Then ___________

a) A⊂B

b) B⊂A

c) C⊂B and A⊂C

d) B⊂C and A⊂C

View Answer

Explanation: Here A has two elements 1 and 3. They both belongs to C so, A⊂C. Here B has three elements 1, 5 and 9. They all belongs to C so, B⊂C.

8. If an element x∈A and A⊂B then x∈B.

a) True

b) False

View Answer

Explanation: If A⊂B then every element of A is in set B. Since x is an element of A so, x also belong to B. x∈B is true.

9. If X∈A and A⊂B then X⊂B.

a) True

b) False

View Answer

Explanation: Let X = {1,2}. A= {{1,2},3}, B= {{1,2},3,4}. Since elements of X does not belongs to set B so, X is not a subset of B. X⊂B is false.

10. Let A = {1, 2, {3, 4}, 5}. Which of the following is true?

a) {3, 4} ⊂ A

b) {3, 4} ∈ A

c) {{3, 4}} ⊂ A

d) {1, 2, 5} ⊂ A

View Answer

Explanation: Here A has elements 1,2, {3,4} and 5. So, {3, 4} ∈ A and {{3, 4}} ⊂ A. {1, 2, 5} ⊂ A. {3, 4} is not subset of A.

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