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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 a `R b` Iff `|a-b| le1.` 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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