Which of the following relations in R is an equivalence relatilon?

x R_{1} y \Leftrightarrow | x | = | y |

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x R_{2} y \Leftrightarrow x \geq y

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x R_{3} y \Leftrightarrow \frac{x}{y}

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x R_{4} y \Leftrightarrow x < y

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Solution

The correct option is A $x R_{1} y \Leftrightarrow | x | = | y |$
It is simple to check that only, $R_{1}$ is an equivalence relation.

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