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In the set X = { a, b, c, d} which of t...

In the set `X = { a, b, c, d}` which of the following relation is a function?

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)}`

Text Solution

Verified by Experts

The correct Answer is:
B
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.
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