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Home » If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B? Give reasons in support of your answer.
If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B? Give reasons in support of your answer.
CBSE | Class 11 | Exercise 2.3 | Maths | RD Sharma | Relations
If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B? Give reasons in support of your answer.

(i) {(1, 6), (3, 4), (5, 2)}

(ii) {(1, 5), (2, 6), (3, 4), (3, 6)}

Solution:

We are given that A = {1, 2, 3} and B = {4, 5, 6}

We can define a relation from A to B in the following manner:

A\text{ }\times \text{ }B=\left\{ 1,\text{ }2,\text{ }3 \right\}\text{ }\times \text{ }\left\{ 4,\text{ }5,\text{ }6 \right\}

A\text{ }\times \text{ }B=\left\{ \left( 1,\text{ }4 \right),\text{ }\left( 1,\text{ }5 \right),\text{ }\left( 1,\text{ }6 \right),\text{ }\left( 2,\text{ }4 \right),\text{ }\left( 2,\text{ }5 \right),\text{ }\left( 2,\text{ }6 \right),\text{ }\left( 3,\text{ }4 \right),\text{ }\left( 3,\text{ }5 \right),\text{ }\left( 3,\text{ }6 \right) \right\}

(i) {(1, 6), (3, 4), (5, 2)}

No, the above-given set of values doesn’t represent a relation from A to B. The set given here is not a subset of A × B. This is because (5, 2) is not a part of the relation defined from A to B.

(ii) {(1, 5), (2, 6), (3, 4), (3, 6)}

Yes, the above-given set of values represents a relation from A to B. The given set is a subset of A × B.

i

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