Let R be a relation on a set A such that R = {R^{ - 1}} , then R is

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1.Relation and Function

easy

Let $R$ be a relation on a set $A$ such that $R = {R^{ - 1}}$, then $R$ is

A

Reflexive

B

Symmetric

C

Transitive

D

None of these

Solution

(b) Let $(a,b) \in R$

Then, $(a,b) \in R \Rightarrow (b,a) \in {R^{ – 1}}$, [By def. of ${R^{ – 1}}$]

==> $(b,a) \in R$,$[\because R = {R^{ – 1}}]$

So, $R$ is symmetric.

Standard 12

Mathematics

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