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

Options

A. reflexive, symmetric and transitive
B. reflexive, transitive but not symmetric
C. symmetric, transitive but not reflexive
D. neither transitive, nor reflexive, not symmetric

Answer

B

Explanation

`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.