First slide

Relations XII

Question

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

Easy

A

Reflexive
B

Symmetric
C

Transitive
D

None of these

Solution

Let $(a, b) \in R \Rightarrow (b, a) \in R^{- 1},$ [By def. or $R^{- 1}]$
$\Rightarrow (b, a) \in R, [∵ R = R^{- 1}]$
So, R is symmetric.

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