5 Recursive Definitions and Structural Induction Consider the following recursive definition of full binary trees:2 Base: A single vertex is a full binary tree, and we call this vertex a root of that tree. Recursive Rule: If v is a single vertex and To and Ti are two ful binary trees with roots respectively vo and v1, then the following is a full binary tree with root v: A vertex v with a left outgoing edge from v to the root of To and a right outgoing edge from v to the root of Ti Let FBT be the set of full binary trees defined by the above recursive definition. Call a vertex in a tree a leaf if it has no outgoing edges, and call it an internal node otherwise. I. Give a recursive definition of function L : FBT N, where L(T) is a number of leaves in full binary tree T. 2. Give a recursive definition of function 1 : FBT N, where I (T) is a number of internal nodes in full binary tree T. 3. Prove using structural induction that L(T)-1(T) + 1 for every T E FBT