A complete binary tree is a graph defined through the following recursive definition. Basis step: A single vertex is a complete binary tree. Inductive step: If T1 and T2 are disjoint complete binary trees with roots r1, r2, respectively, the the graph formed by starting with a root r, and adding an edge from r to each of the vertices r1, r2 is also a complete binary tree. The set of leaves of a complete binary tree can also be defined recursively. Basis step: The root r is a leaf of the complete binary tree with exactly one vertex r. Inductive step: The set of leaves of the tree T built from trees T1, T2 is the union of the sets of leaves of T1 and the set of leaves of T2. The height h(T) of a binary tree is defined in the class. Use structural induction to show that `(T), the number of leaves of a complete binary tree T, satisfies the following inequality `(T) 2 h(T)

A complete binary tree is a graph defined through the following recur- sive definition Basis step: A single vertex is a complete binary tree Inductive step: If Ti and T2 are disjoint complete binary trees with roots ri, 2, respectively, the the graph formed by starting with a root r, and adding an edge from r to each of the vertices ri, r2 is also a complete binary tree The set of leaves of a complete binary tree can also be defined recur sively Basis step: The root r is a leaf of the complete binary tree with exactly one vertex r Inductive step: The set of leaves of the tree T built from trees Ti, T2 is the union of the sets of leaves of Ti and the set of leaves of T2 The height h(T) of a binary tree is defined in the class. Use structural induction to show that ((T), the number of leaves of a complete binary tree T, satisfies the following inequality (T)2h(T)