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x^2=xy is a relation which is:

Question

$x^{2} = x y$ is a relation which is:

Symmetric

Reflexive

Transitive

All of these

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Levi Discussed

x^{2} = x y

is a relation which is:

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Text solutionVerified

x R x \Rightarrow x^{2} = x . x

Hence reflexive

x R y \Rightarrow x^{2} = x y . \Rightarrow x = y

y R x \Rightarrow y^{2} = x y \Rightarrow y = x

Hence symmetric

x R y

and

y R z

\Rightarrow x^{2} = x y \Rightarrow x = y .

Also

y^{2} = yz \Rightarrow y = z

Since

x = z, x . x = z . x \Rightarrow x^{2} = x z \Rightarrow x R z

. Hence transitive.

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