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.

Question

Philoid · Accepted Answer

Given,

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

A relation from A to B can be defined as:

A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}

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

No, it is not a relation from A to B. The given set is not a subset of A × B as (5, 2) is not a part of the relation from A to B.

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

Yes, it is a relation from A to B. The given set is a subset of A × B.

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

No, it is not a relation from A to B. The given set is not a subset of A × B as (4, 2), (4, 3), (5, 1) are not a part of the relation from A to B.

iv. A × B

A × B is a relation from A to B can be defined as:

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