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

Answer 2

Let $( a , b ) \in R$

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

⇒ $( b , a ) \in R$, $\left[ \because R = R ^ { - 1 } \right]$ So, R is symmetric.