Consider any $a,b,c \in Z.$

1. Since $a-a=0=3.0\Rightarrow(a-a)$ is divisible by 3.

   $\Rightarrow(a,a)\in R \Rightarrow$ is reflexive.

2. Let $(a,b)\in R \Rightarrow (a-b)$ is divisible by 3.

   $\Rightarrow a-b=3q$ for some $q \in Z\Rightarrow b-a=3(-q)$

   $\Rightarrow (b-a)$ is divisible by 3 $\hspace{8cm}(\because q\in Z \Rightarrow -q \in Z \Rightarrow -q \in Z)$ …