The relation "congruence modulo m" is: | vedclass

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(D) Let $R$ be the relation defined on the set of integers $\mathbb{Z}$ such that $aRb$ if and only if $a \equiv b \pmod{m}$,which means $a - b$ is di

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An equivalence relation

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(D) Let $R$ be the relation defined on the set of integers $\mathbb{Z}$ such that $aRb$ if and only if $a \equiv b \pmod{m}$,which means $a - b$ is divisible by $m$.$1$. Reflexivity: For any $a \in \mathbb{Z}$,$a - a = 0$,which is divisible by $m$. Thus,$aRa$ holds.$2$. Symmetry: If $aRb$,then $a - b = km$ for some integer $k$. Then $b - a = -(km) = (-k)m$. Since $-k$ is an integer,$bRa$ holds.$3$. Transitivity: If $aRb$ and $bRc$,then $a - b = km$ and $b - c = lm$ for some integers $k, l$. Adding these,$a - c = (k + l)m$. Since $k + l$ is an integer,$aRc$ holds.Since the relation is reflexive,symmetric,and transitive,it is an equivalence relation.

The relation "congruence modulo $m$" is:

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