Consider the directed graph G with vertex set V as diagrammed:
Let $R^+$ be the binary relation on V given by $iR^+j$ whenever there is a walk in G from i to j. $R^+$ is an equivalence relation for this graph.
What is the partition of V defined by the equivalence relation $R^+$?
{1}, {2}, {3}, {4}, {5}, {6}, {7}, {8}
{1,5}, {2,6}, {3,7}, {4,8}
{1,2,3,4}, {5,6,7,8}
{1, 2, 3, 4, 5, 6, 7, 8}