Any help or sort of input on this question would help a great deal. Thanks
Let $m\in N$. Recall for any integer $n \in Z$, the definition of $[n]$ in $Z_m$ is $[n] = \{x | x \equiv n \pmod m\}$. Prove that $Z_m$, for any $a, b, \in Z$, either $[a] = [b]$ or $[a]\cap [b] = \emptyset$.