The set of full binary trees can be de ned recursively: (a) The tree with only one vertex is a full binary tree. (b) If T1 and T2 are two disjoint full binary trees, there is a full binary tree, denoted as T1 T2, with T1 as its left subtree, T2 as its right subtree, and a new root r connecting to T1 and T2. Use structural induction to prove that the number of leaves is one more than the number of internal vertices in a full binary tree.

Bigmart supermarket has different ways of awarding discounts to its customers for each purchase they make. an 8 percent discount is given on the total value of the purchase. in addition, a standard loyalty discount is given if customers have a permanent customer id card. your program should indicate the amount payable by the customer after the discounts. identify the inputs that the program requires from these options: i. the discount percentage ii. the total value of the purchase iii. the loyalty-discount amount iv. the customer id card number v. the amount payable after discount