Show that the relation \( R \) on the set \( \mathbf{I} \) of all integers defined by \( R=\{(a,...

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Show that the relation \( R \) on the set \( \mathbf{I} \) of all integers defined by \( R=\{(a, b): a-b \) is divisible by \( 3, a, b \in I\} \) is an equivalence relation.
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