First slide

Relations XII

Question

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

Moderate

A

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

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

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

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

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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