A complete binary tree is defined inductively as follows. A complete binary tree of height 0 consists of 1 node which is the root. A complete binary tree of height h + 1 consists of two complete binary trees of height h whose roots are connected to a new root. Let T be a complete binary tree of height h. Prove that the number of leaves of the tree is 2h and the size of the tree (number of nodes in T ) is 2h+1 1.