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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

anti-symmetric only

Text Solution

Verified by Experts

The correct Answer is:
A
`because|a-a|=0lt1impliesaRa,AAainR`
`therefore` R is reflexive
Again, aRb implies `|a-b|le1`
`implies |b-a|le1impliesbRa`
`therefore` R is symmetric.
Again, 1 R 2 and 2R1 but `2 ne 1`
`therefore` R is not anti-symmetric
Further, 1R2 and 2R3 but `1 cancelR 3" "[because|1-3|=2gt1]`
`therefore` R is not transitive.
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