# Mathematics Questions and Answers – Relations

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

1. A relation is a subset of cartesian products.
a) True
b) False

Explanation: A relation from a non-empty set A to a non-empty set B is a subset of cartesian product A X B. First element is called the preimage of second and second element is called image of first.

2. Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the domain.
a) {1,2,3,4,5}
b) {2,3,4,5}
c) {1,2,3,4}
d) {1,2,3,4,5,6}

Explanation: We know, domain of a relation is the set from which relation is defined i.e. set A.
So, domain = {1,2,3,4,5}.

3. Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the codomain.
a) {1,2,3,4,5}
b) {2,3,4,5}
c) {1,2,3,4}
d) {1,2,3,4,5,6}

Explanation: We know, codomain of a relation is the set to which relation is defined i.e. set A.
So, codomain = {1,2,3,4,5}.

4. Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the range.
a) {1,2,3,4,5}
b) {2,3,4,5}
c) {1,2,3,4}
d) {1,2,3,4,5,6}

Explanation: Range is the set of elements of codomain which have their preimage in domain.
Relation R = {(1,2), (2,3), (3,4), (4,5)}.
Range = {2,3,4,5}.

5. If set A has 2 elements and set B has 4 elements then how many relations are possible?
a) 32
b) 128
c) 256
d) 64

Explanation: We know, A X B has 2*4 i.e. 8 elements. Number of subsets of A X B is 28 i.e. 256.
A relation is a subset of cartesian product so, number of possible relations are 256.

6. Is relation from set A to set B is always equal to relation from set B to set A.
a) True
b) False

Explanation: A relation from a non-empty set A to a non-empty set B is a subset of cartesian product A X B. A relation from a non-empty set B to a non-empty set A is a subset of cartesian product B X A.
Since A X B ≠ B X A so, both relations are not equal.

7. If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y2}. Find domain of the relation.
a) {1,4,9}
b) {-1,1, -2,2, -3,3}
c) {1,4,8,9}
d) {-1,1, -2,2, -3,3,5}

Explanation: We know, domain of a relation is the set from which relation is defined i.e. set A.
So, domain = {1,4,8,9}.

8. If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y2}. Find codomain of the relation.
a) {1,4,9}
b) {-1,1, -2,2, -3,3}
c) {1,4,8,9}
d) {-1,1, -2,2, -3,3,5}

Explanation: We know, codomain of a relation is the set to which relation is defined i.e. set B.
So, codomain = {-1,1, -2,2, -3,3,5}.

9. If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y2}. Find range of the relation.
a) {1,4,9}
b) {-1,1, -2,2, -3,3}
c) {1,4,8,9}
d) {-1,1, -2,2, -3,3,5}

Explanation: Range is the set of elements of codomain which have their preimage in domain.
Relation R = {(1,1), (1, -1), (4,2), (4, -2), (9,3), (9, -3)}.
Range = {-1,1, -2,2, -3,3}.

10. Let A={1,2} and B={3,4}. Which of the following cannot be relation from set A to set B?
a) {(1,1), (1,2), (1,3), (1,4)}
b) {(1,3), (1,4)}
c) {(2,3), (2,4)}
d) {(1,3), (1,4), (2,3), (2,4)}

Explanation: A relation from set A to set B is a subset of cartesian product of A X B. In ordered pair, first element should belong to set A and second element should belongs to set B.
In {(1,1), (1,2), (1,3), (1,4)}, 1 and 2 should also be in the set B which is not so as given in question.
Hence, {(1,1), (1,2), (1,3), (1,4)} is not a relation from set A to set B.

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

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