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.
(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.