If A = {3, 5, 7, 9} and B = {a, b, c}, then which of the following are relations from A to B ? Give reasons for your answer.
(i) `R_(1) = {(3, a), (5, b), (5, c)}`
(ii) `R_(2) = {(3, c), (9, b), (5, a)}`
(iii) `R_(3) = {(3, c), (b, c), (7, b), (9, a)}`
(iv) `R_(4) = {(3, b), (7, c), (c, a), (b, 9)}`

Explanation

`A xx B = {(3, a), (3, b), (3, c), (5, a), (5, b), (5, c), (7, a), (9, a), (9, b), (9, c)}`
(i) Since `R_(1)` is a subset of `A xx B`. So `R_(1)` is a relation from A to B.
(ii) Since `R_(2)` is a subset of `A xx B`. So, `R_(2)` is a relation from A to B.
(iii) Here, (b, c) `in A xx B`. So, `R_(3)` is not a subset of `A xx B` and hence `R_(3)` is not a relation from A to B.
(iv) Since `A xx B` does not contain (c, a) and (b, 9), so `R_(4)` is not a relation from A to B