solve the whole question.

Using induction, prove that "A complete binary tree of height h has 2^h + 1 - 1 nodes". Build the Max-Heap from the following dataset: [8, 7, 9, 5, 2, 15]. Show each step of your calculation Show Delete-Max-Heap on the following heap: [6, 3, 5, 1, 2, 4]. (one complete operation by showing each intermediate step) List the time complexity of the following operations for a BST and a Heap data structure a. Insert b. Delete c. Search d. Print List some applications of Binary Tree and Heap