2.a: Prove by induction that any tree T(V,E) on n vertices contains exactly n1 edges. (2 points) Remark 4. Let's assume that T has n2 vertices, and m edges. Since T is connected and has two vertices, say u and v, there is at least one path from u to v. Let (u,w) be the first edge on this path (w could be v). Remove this edge. Since a tree is minimally connected, removing this edge would disconnect the tree. Apply induction on the connected components of the forest obtained from T by removing (u,w). A connected component of an undirected graph is a subset CV of vertices which are all connected to each other by paths, and they are not connected to any other vertex outside C (that is, to any vertex in V\C)