Question:
A relation R on a set A is a symmetric relation if __________.
Solution:
A relation R on a set A is symmetric relation
i.e if $(x, y) \in R$ for $x, y \in A$
$\Leftrightarrow(y, x) \in R$
i.e if $(x, y) \in R$
$\Leftrightarrow(x, y) \in R^{-1}$
$\therefore R=R^{-1}$
Hence relation R on a set A is symmetric
If $R=R^{-1}$
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