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Question

Let $R$ be a relation on a set $A$ such that $R equals R to the power of negative 1 end exponent comma$ then $R$ is

(a) Reflexive
Symmetric
Transitive
None of these

The correct answer is: Symmetric

Let $open parentheses a comma b close parentheses element of R.$ Then,
$left parenthesis a comma b right parenthesis element of R rightwards double arrow left parenthesis b comma a right parenthesis element of R to the power of negative 1 end exponent$ [By def. of $R to the power of negative 1 end exponent$ ]
$rightwards double arrow left parenthesis b comma a right parenthesis element of R$ $left square bracket because R equals R to the power of negative 1 end exponent right square bracket$
So, $R$ is symmetric

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