The relation "congruence modulo m" is | vedclass

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(D) Let $R$ be a relation defined as $x R y \iff x - y$ is divisible by $m$.$1$. Reflexivity: For any $x$,$x - x = 0$,which is divisible by $m$. Thus,

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An equivalence relation

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(D) Let $R$ be a relation defined as $x R y \iff x - y$ is divisible by $m$.$1$. Reflexivity: For any $x$,$x - x = 0$,which is divisible by $m$. Thus,$x R x$ holds. So,it is reflexive.$2$. Symmetry: If $x R y$,then $x - y = km$ for some integer $k$. Then $y - x = -(km) = (-k)m$,which is also divisible by $m$. Thus,$y R x$ holds. So,it is symmetric.$3$. Transitivity: If $x R y$ and $y R z$,then $x - y = k_1 m$ and $y - z = k_2 m$ for some integers $k_1, k_2$. Adding these,$(x - y) + (y - z) = x - z = (k_1 + k_2)m$. Since $(k_1 + k_2)$ is an integer,$x - z$ is divisible by $m$. Thus,$x R z$ holds. So,it is transitive.Since the relation is reflexive,symmetric,and transitive,it is an equivalence relation.

The relation "congruence modulo $m$" is

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