Question

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

Answer 1

Answer: (B)

symmetric

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 symmetric.