This problem will concern operations on the AVL tree T shown in the figure below.

a) Show that T is an AVL tree by writing in the balance at each node. b) Draw the tree after performing operation insert(4). Indicate any rotations that are required at each step. c) Draw the original tree after performing operation delete(8). Swap with its predecessor. It suffices to just draw the final tree. d) Draw the original tree after performing operation delete(8). This time, swap with its successor. It suffices to just draw the final tree.

25 28 15 26 30 20 27 12 17 21 13