Let A = {2, 3, 5, 8} and B = {4, 27, 125, 512}, then which of the following are relations from A to B ? Give reasons for your answer.
(i) `R_(1) = {(2, 4), (3, 125), (8, 512)}`
(ii) `R_(2) = {(2, 125), (512, 8), (3, 27)}`
(iii) `R_(3) = {(2, 512), (3, 125), (3, 4)}`
(iv) `R_(4) = {(2, 512), (3, 125), (3, 4)}`

Explanation

(i) `R_(1) sube A xx B`, so `R_(1)` is a relation from A to B
(ii) `R_(2) cancelsube A xx B`, so `R_(2)` is not a relation from A to B
(iii) `R_(3) cancelsube A xx B`, so `R_(3)` is not a relation from A to B
(iv) `R_(4) sube A xx B`, so `R_(4)` is a relation from A to B