Prove that the relation on Z (integer) define by a~b iff a – b is divisible by 5. is an equivalence relation.
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Another little help:
Reflexive: For all $\displaystyle a\in\mathbb{Z}$ we have
$\displaystyle a-a=0=5\cdot 0$ that is, $\displaystyle a-a$ is divisible by $\displaystyle 5$ which means that $\displaystyle a\sim a$
Try the rest.