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Let S be set of all real numbers and...

Let S be set of all real numbers and let R be relation on s , defined by `a R b hArr |a-b|le 1.` then R is

A

symmetric and transitive but not reflexive

B

reflexive and transitive but not symmetric

C

reflexive and symmetric but not transitive

D

an equivalence relation

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `"aRb "iff|a-b|le1`
Reflexive `"aRa "=|a-a|=0le1`
So, it is reflexive.
Symmetric `"aRb "iff|a-b|le1`
`implies" "|b-a|le1," i.e., ""aRb"implies"bRa"`
So, it is symmetric.
Transitive Take a = 1, b = 2 and c = 3
`{:("Now,",,,|a-b|=|1-2|=1),("and",,,|b-c|=|2-3|=1),("But",,,|a-c|=|1-3|=2gt1):}`
which is not true.
i.e., `" ""aRb","bRc cancelimplies "aRc"`
So, it is not transitive.
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