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If R is a relation defined as aRb, "iff"...

If R is a relation defined as aRb, `"iff"|a-b|gt0`, then the relation is

A

reflexive

B

symmetric

C

transitive

D

symmetric and transitive

Text Solution

Verified by Experts

The correct Answer is:
D
Since, R is defined as aRb, iff `|a-b|gt0`.
Reflexive aRa, `"iff"|a-a|gt0`,
which is not true. So, R is not reflexive.
Symmetric a Rb, `"iff"|a-b|gt0`
Now, bRa `"iff,"|b-a|gt0`
`because" "|a-b|gt0implies|b-a|gt0`
`:." "bRa`
Thus, R is symmetric.
Transitive aRb, `"iff"|a-b|gt0`
`bRc,"iff"|b-c|gt0implies|a-b+b-c|gt0`
`implies" "|a-c|gt0`
`:." "aRc`
Thus, R is also transitive.
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