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Nutan Wali
Asked: 2022-11-09T10:18:32+05:30 In:

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

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
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  1. Correct Answer – 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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