Which one of following relations on R is an equivalence relation

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1.Relation and Function

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

A

$a\,{R_1}\,b \Leftrightarrow |a| = |b|$

B

$a{R_2}b \Leftrightarrow a \ge b$

C

$a{R_3}b \Leftrightarrow a \ {\rm{ divides }}\ b$

D

$a{R_4}b \Leftrightarrow a < b$

Solution

$a R_1 b \Leftrightarrow|a|=|b|$

$a=b$

$R_1$ is a reflexive symmetric and transitive. ( as we know $a=b$ )

$\therefore(a, a)$ is present

$\therefore(a, b)(b, a)$ will also be present.

So it is an equivalence relation .

Standard 12

Mathematics

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