2. Red-Black Tree [20 pt] a. Prove by induction on the black height of x (bhx)) that a subtree rooted at x has at least 2blo-1 internal nodes for a red-black tree. A post-order traversal of a red-black tree on the numbers 1 to 15 gives the following colors: R R B B B B B R B R R B R B B. Produce the tree. bhx) b