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Question

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)}

(iii) {(4, 2), (4, 3), (5, 1)}

(iv) A×B.

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Solution

(i) We have,

A = {1, 2, 3} and B = {4, 5, 6}

{(1, 6), (3, 4), (5, 2)} is not a relation from A to B as it is not a subset of A×B.

(ii) We have,

A = {1, 2, 3} and B = {4, 5, 6} {(1, 5), (2, 6), (3, 4), (3, 6)} is subset of A×B, so it is a relation from A to B.

(iii) We have,

A = {1, 2, 3} and B = {4, 5, 6} {(4, 2), (4, 3), (5, 1)} is not a relation from A to B as it is not a subset of A×B.

(iv) We have,

A = {1, 2, 3} and B = {4, 5, 6}

A×B is a relation from A to B.


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