2. Recall that an equivalence relation must be reflexive, symmetric and transitive. If you are having trouble remembering how to check these properties from the directed graph, refer back to the definitions in section 10.2.
If R is an equivalence relation, then the graph will consist of separate groups of vertices (that is, the vertices will occur in groups for which no vertices from different groups are conncected by an edge but all vertices within a group have loops on them and are connected in all possible ways). These groups give you the partition of the set A and hence the equivalence classes of A. In a sense, all the vertices within a group are equivalent since they are related in all possible ways to all the vertices within that group.