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Let S be the set of all real numbers a...

Let S be the set of all real numbers and Let R be a relations on s defined by `a R B hArr |a|le b.` then ,R is

A

Reflexive

B

Symmetric

C

Transitive

D

Equivalence

Text Solution

Verified by Experts

The correct Answer is:
C
(i) Reflexive R is not reflexive `|a| le a` is not true for `a lt 0`
(ii) Symmetric R is not symmetric `aRB rArr |a| le b rArr |b| le a` is not true for ` a lt 0`
(iii) Transitive R is transitive `aRb rArr |a| le b," for some "a,b, in R`
`bRc rArr |b| le c`
From (i) and (ii), we get
`|a| le b le |b| le c rArr |a| le c rArr aRc.`
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