In the set X = {a, b, c, d}, which of the following functions in X?

Options

A. `R_(1) = {(b, a), (a, b), (c, d), (a, c)}`
B. `R_(2) = {(a, d), (d, c), (b, b), (c, c)}`
C. `R_(3) = {(a, b), (b, c), (c, d), (b, d)}`
D. `R_(4) = {(a, a), (b, b), (c, c), (a, d)}`

Answer

B

Explanation

X = {a, b, c, d}
`R_(1)` = {(b, a), (a, b), (c, d), (a, c)}
`(a, b) in R_(1) and (a, c) in R`,
`therefore R_(1)` is not a function.
`R_(2) = {(a, d), (d, c), (b, b), (c, c)}`

Here, `R_(2)` is a function.