10. The sets of leaves and internal vertices of a full binary tree can be defined recursively.
Basis step: The root r is a leaf of the full binary tree with exactly one vertex r.
This tree has no internal vertices.
Recursive step: The set of leaves of the tree T = T1 · T2 is the union of the sets of leaves of T1 and of T2. The internal vertices of T are the root r of T and the union of the set of internal vertices of T1 and the set of internal vertices of T2.
Use structural induction to show that l(T), the number of leaves of a full binary tree T, is 1 more than i(T), the number of internal vertices of T.