4. [16 pts] Recall the recursive definitions n(T) and h(T) of the number of nodes and height, respectively, of a full binary tree. Further, consider the following recursive definitions of the set of leaves and the set of internal nodes of a full binary tree: The root r is a leaf of the full binary tree with exactly one node r. This tree has no internal nodes. The set of leaves of the tree T-TiT2 is the union of the sets of leaves of T1 and of T2. The internal nodes of T are the root r of T and the union of the sets of internal nodes of Ti and of T2 o Denote by (T) and i(T) the numbers of leaves and of internal nodes, respectively, of a full binary tree T. Use structural induction to prove the following two results on full binary trees . 1. n(T) 2 2h(T) 1