If R is a symmetric relation on a set A, then write a relation between

Here, R is symmetric on the set A.

Let $(a, b) \in R$

$\Rightarrow(b, a) \in R$                                 [Since $R$ is symmetric]

$\Rightarrow(a, b) \in R^{-1}$                         [By definition of inverse relation

$\Rightarrow R \subset R^{-1}$

Let $(x, y) \in R^{-1}$

$\Rightarrow(y, x) \in R$                                         [By definition of inverse relation]

$\Rightarrow(x, y) \in R$                                         [Since $R$ is symmetric]

$\Rightarrow R^{-1} \subset R$

Thus, $R=R^{-1}$