Question

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

• A. a reflexive relation
• B. a symmetric relation
• C. a transitive relation
• D. None of the above

Answer 1

The correct option is B a symmetric relation

Let $(a,b)\in R$
Then, $(a,b)\in R\Rightarrow (b,a)\in R^{-1}$,
$[$ by def. of $R^{-1}]$ $\Rightarrow (b,a)\in R,[\because R=R^{-1}],$ so $R$ is a symmetric relation.