Let $A=\{0,1,2,3\}$ and $R$ a relation over $A$ :
$$
R=\{(0,0),(0,1),(0,3),(1,1),(1,0),(2,3),(3,3)\}
$$
Draw the directed graph of $R$. Check whether $R$ is an equivalence relation. Give a counterexample in each case in which the relation does not satisfy one of the properties of being an equivalence relation.