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Let R be a relation defined by R = {(a, ...

Let R be a relation defined by R = {(a, b) : `a ge b`}, where a and b are real numbers, then R is

A

reflexive, symmetric and transitive

B

reflexive, transitive but not symmetric

C

symmetric, transitive but not reflexive

D

neither transitive, nor reflexive, not symmetric

Text Solution

Verified by Experts

The correct Answer is:
B
`R = {(a, b) : a ge b}`
We know that, `a ge a`
`therefore (a, a)inR, AAainR`
R is a reflexive relation.
Let `(a, b) in R`
`implies a ge b`
`cancelimplies b le a`
`cancelimplies (b, a) in R`
So, R is not symmetric relation.
Now, let (a, b) `in R` and (b, c) `in` R.
`implies a ge b and b ge c`
`implies a ge c`
`implies (a, c) in R`
`therefore` R is a transitive relation.
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