Questions

Let ${\mathrm{R}}_{1}$ be a relation defined by $\mathrm{R\_}1=\left\{\left(\mathrm{a},\mathrm{b}\right)\right|\mathrm{a}\ge \mathrm{b},\mathrm{a},\mathrm{b}\in \mathrm{R}\}.$ Then ${\mathrm{R}}_{1}$ is

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By Expert Faculty of Sri Chaitanya

a

An equivalence relation on R

b

Reflexive, transitive but not symmetric

c

Symmetric, Transitive but not reflexive

d

Neither transitive not reflexive by symmetric

NEW

detailed solution

Correct option is B

For any a∈R, we have a≥a, therefore the relation R is reflexive but it is not symmetric as (2, 1)∈R but (1, 2)∉R. The relation R is transitive also, because (a, b)∈R, (b, c)∈R imply that a≥b and b≥c which is turn imply that a≥c.

Similar Questions

Let R be a reflexive relation on a finite set A having elements, and let there be m ordered pairs in R. Then

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