Which one of the following relations on R is | vedclass

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

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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.For $R_1: a R_1 b \Leftrightarrow |a| = |b|$.$1$. Reflexive: $|a| = |a|$ is true for all $a \in R$,so $(a, a) \in R_1$.$2$. Symmetric: If $|a| = |b|$,then $|b| = |a|$,so if $(a, b) \in R_1$,then $(b, a) \in R_1$.$3$. Transitive: If $|a| = |b|$ and $|b| = |c|$,then $|a| = |c|$,so if $(a, b) \in R_1$ and $(b, c) \in R_1$,then $(a, c) \in R_1$.Since $R_1$ satisfies all three properties,it is an equivalence relation.$R_2$ is not symmetric ($2 \ge 1$ but $1 
ot\ge 2$).$R_3$ is not symmetric ($2 	ext{ divides } 4$ but $4 	ext{ does not divide } 2$).$R_4$ is not reflexive ($a < a$ is false).

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

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