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Question

Let R be the realtion on the set R of all real

numbers defined by a R b if |a-b| 1. then R is


A

Reflexive and Symmetric

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B

Symmetric only

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C

Transitive only

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D

Anti-symmetric only

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Solution

The correct option is A

Reflexive and Symmetric


|a - a| = 0 < 1 a R a ∀ a R

R is reflexive.

Again a R b |a-b| 1|ba|1bRa
R is symmetric, Again 1R12 and 12RI but 121
R is not anti - symmetric
Further, 1R2 and 2R3 [|13|=2>1]
R is not transitive.


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