Exercise 3. Let G be a connected graph, with vertex set V. The distance between two vertices u and v, denoted dist(u, v), is defined as the minimal length of a path joining u to v. Show that the following properties hold, for any u,v, w V: (i) dist(u, v> 0, and dist(u, v) = 0 if and only if u = v (ii) dist(u,v) = dist(v, u) (iii) dist(u, v) dist(u, u) + dist (u, u)