Let R be the relation on the set R of al...

Let R be the relation on the set R of all real numbers defined by aRb iff |a-b| `le` 1. Then, R is

A

Reflexive and symmetric

B

Symmetric only

C

Transitive only

D

None of these

Text Solution

Verified by Experts

The correct Answer is:

A

`|a-a|=0 lt 1 :. aRa AA a in R`
Therefore, R is reflexive.
Again `aRbimplies |a-b| le 1" and " |b-a| le 1 implies bRa`
Therefore, R is symmetric.
Therefore, R is not anti-symmetric.
Further, `1R2 and 2R3" but " 1 cancel(R ) 3 [ :' |1-3|=2 gt 1]`
Therefore, R is not transitive.

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