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Which one of the following relations on R is an equivalence relation?

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$a R_{1} b \Leftrightarrow | a | = | b |$

$a R_{2} b \Leftrightarrow a \geq b$

$a R_{3} b \Leftrightarrow a divides b$

$a R_{4} b \Leftrightarrow a < b$

answer is A.

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Detailed Solution

$a R_{1} b \Leftrightarrow | a | = | b | satisfies.$

Inequality operation can't be reflective, symmetric

so it is not equivalence

but equality is reflexive, symmetric, and transitive

so this relation is equivalence

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