Suppose that g = (v, e) is a directed graph. a vertex w ∈ v is reachable from a vertex v ∈ v if there is a directed path from v to w. the vertices v and w are mutually reachable if there are both a directed path from v to w and a directed path from w to v in g.

show that { (u, v) | u and v are mutually reachable in directed graph g = (v, e) } is an equivalence relation (i. e., reflexive, symmetric, and transitive).