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Question

Let $P equals open curly brackets open parentheses x comma y close parentheses vertical line x to the power of 2 end exponent plus y to the power of 2 end exponent equals 1 comma x comma y element of R close curly brackets.$ Then, $P$ is

Reflexive
Symmetric
Transitive
Antisymmetric

The correct answer is: Symmetric

Obviously the relation is not reflexive and transitive but it is symmetric, because
$x to the power of 2 end exponent plus y to the power of 2 end exponent equals 1 rightwards double arrow y to the power of 2 end exponent plus x to the power of 2 end exponent equals 1$

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