Page 278-9 Exercise 8

The definition in the text states that "A tree is a finite set of one or more nodes such that 1) there is a specially desig­
nated node called the root; 2) the remaining nodes are partitioned into n ≤ 0 disjoint sets T₁, ... ,T_nwhere each of these sets is a
tree. T_{1, ... ,Tn are called the subtrees of the root."}

This definition is equivalent to statement c since the condition that T₁, ... ,T_n be disjoint sets means that there can be only one path between any two vertices.  Since the sets are disjoint there can be no cross-edges in the graph. This means that
there can not be multiple paths between vertices.

Statement c implies statement d because a connected graph with cross-edges must have more than n edges, and hence is cyclic.  Therefore, the graph must be acyclic, and contain n-1 edges.

Statement d implies statement b because removing an edge from a  cyclic graph produces a connected graph.  Since the graph is not cyclic, removing an edge must produce a graph that is not connected.  In essence, all nodes except leaf nodes are articula­
tion points.