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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. (iii) {(4, 2), (4, 3), (5, 1)} (iv) A × B
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. (iii) {(4, 2), (4, 3), (5, 1)} (iv) A × B
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. (iii) {(4, 2), (4, 3), (5, 1)} (iv) A × B

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\}

(iii) {(4, 2), (4, 3), (5, 1)}

No, the above-given set of values doesn’t represent a relation from A to B. The given set is clearly not a subset of A × B.

(iv) A × B

A × B is clearly a relation from A to B. This relation can be defined as follows:

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\}

 

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