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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Similar questions

Q. In the set Z of all integers, which of the following relation R is not an equivalence relation?
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Which of the following relations in R is an equivalence relatilon?

The correct option is A xR1 y⇔|x|=|y|It is simple to check that only, R1is an equivalence relation.

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.