First slide

Relations XII

Question

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

Moderate

A

Reflexive
B

Symmetric
C

Transitive
D

None of these

Solution

$\begin{array}{l} Let (a, b) \in R \\ If (a, b) \in R \\ \Rightarrow (b, a) \in R^{- 1}, [By def of R^{- 1}] \\ \Rightarrow (b, a) \in R, [∵ R = R^{- 1}] \end{array}$
So, R is symmetric

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