(10 marks) In this question, as in class, we consider a leaf node in an AVL tree to have height 1. (a) (4 marks) Prove that if an AVL tree T has a...

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2. (10 marks) In this question, as in class, we consider a leaf node in an AVL tree to haveheight 1. (a) (4 marks) Prove that if an AVL tree T has a height of at most 2, then its numberof leaf nodes is strictly greater than one-third its total number of nodes. (b) (6 marks) Use induction on the height h(T) of the tree to prove that for any AVLtree T, the number of leaf nodes is strictly greater than one-third the total numberof nodes.