The set of full binary trees can be de ned recursively: (a) The tree with only one vertex is a full binary tree. (b) If T1 and T2 are two disjoint full binary trees, there is a full binary tree, denoted as T1 T2, with T1 as its left subtree, T2 as its right subtree, and a new root r connecting to T1 and T2. Use structural induction to prove that the number of leaves is one more than the number of internal vertices in a full binary tree.