Neat handwriting only please and wrote out each step for the proof (Base Step, IH and Inductive Step)

4. (10 points) The set of full binary trees is defined recursively in Definition 5 on page 353: (1.) Basis step: A single vertex r is a rooted tree. e step: If Ti and T2 are disjoint ful binary trees, there is a full binary tree, denoted by Ti - T2, consisting of a (new) root r together with edges connecting this root to the roots of the left subtree Ti and the right subtree T2. The book includes these pictures of the full binary trees that can be built up by applying the recursive step one or two times. (a.) Draw all the binary trees that could be built up by applying the recursive step three (b.) Come up with a formula for the maximum number of nodes (vertices) in a full binary times. tree that is built up by applying the recursive step n times. Prove your formula using mathematical induction