A full binary tree is defined as follows. 1. A single vertex is a full binary tree, and the vertex is called the root. 2. If T1 and T2 are full binary trees with roots r1 and r2, respectively, then the binary tree constructed below is a full binary tree with root r. The circles represent the full binary trees T1 and T2. Prove that a full binary tree has an even number of edges. (Use proof by induction)