A relation R on a set A is a symmetric relation if __________.

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Solution

A relation R on a set A is symmetric relation
i.e if (x, y) $\in$ R for x, y $\in$ A
⇔ (y, x) $\in$ R
i.e if (x, y) $\in$ R
⇔ (x, y) $\in$ R ⁻¹
$∴$ R = R⁻¹
Hence relation R on a set A is symmetric
If R = R⁻¹

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