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

MCQ

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

A
Reflexive
✓
Symmetric
C
Transitive
D
None of these

✓

Answer

Correct option: B.

Symmetric

b
(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.

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