In this problem, you will develop a new proof that every tree with two or more vertices has a leaf. here is an outline for your proof. a. first prove, using strong induction and the fact that every edge of a tree is a cut edge (theorem 50.5), that a tree with n vertices has exactly n # 1 edges. note that our previous proof of this fact (theorem 50.9) used the fact that trees have leaves; that is why we need an alternative proof. b. use (a) to prove that the average degree of a vertex in a tree is less than 2. c. use (b) to prove that every tree (with at least two vertices) has a leaf.