Which of the following relations R is an equi | vedclass

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(A) relation $R$ is an equivalence relation if it is reflexive,symmetric,and transitive. $1$. For $R_1$: $a \, R_1 \, b \Leftrightarrow |a| = |b|$. -

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

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(A) relation $R$ is an equivalence relation if it is reflexive,symmetric,and transitive. $1$. For $R_1$: $a \, R_1 \, b \Leftrightarrow |a| = |b|$. - Reflexive: $|a| = |a|$ is true for all $a$,so $a \, R_1 \, a$. - Symmetric: If $|a| = |b|$,then $|b| = |a|$,so $b \, R_1 \, a$. - Transitive: If $|a| = |b|$ and $|b| = |c|$,then $|a| = |c|$,so $a \, R_1 \, c$. Since $R_1$ satisfies all three properties,it is an equivalence relation. $2$. $R_2$ $(a \ge b)$ is not symmetric (e.g.,$2 \ge 1$ but $1 
ot\ge 2$). $3$. $R_3$ ($a$ is divisible by $b$) is not symmetric (e.g.,$4$ is divisible by $2$,but $2$ is not divisible by $4$). $4$. $R_4$ $(a Thus,the correct option is $A$.

Which of the following relations $R$ is an equivalence relation?

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