* Problem 4: Binary Trees 20 This problem concerns integer-labeled binary trees. A binary tree T is defined recursively as one of two kinds of nodes. T is either an leaf or an internal vertex. A leaf is a 1-tuple (n) where n is an integer. An internal vertex is a 3-tuple (Ti, n, Tr) where Ti and Tf are trees, and n is an integer. The size of a tree T, written T], is the total number of nodes in the tree. We use l(T) to denote the number of leaves of T, and i(T) to denote the number of internal vertices of T. Use strong induction to prove the following claim. Claim 2. For every n 1 and every binary tree T where T, the number of leaves in T is one more than the number of internal vertices of T: i.e. l(T)-i(T) 1