Question

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

• A. Reflexive
• B. Symmetric
• C. Transitive
• D. None of these

Answer 1

The correct option is B

Symmetric

Explanation For The Correct Option:

Determining the correct option

Let $(a,b)\in R$

Therefore, $(b,a)\in R^{-1}$

Since $R=R^{-1}$

Then,$(b,a)\in R^{}$

As $(a,b)\in R\Rightarrow (b,a)\in R$, for all $(a,b)\in A$

Thus the given relation is symmetric if $R=R^{-1}$

Hence, option (B) is the correct answer.