1. Write a proof by induction to show the correctness of the binary search code given below: // Find index of x in sorted array A[p..r]. Return -1 if x is not in A[p..r]. int binarySearch ( A, p, r, x): // Pre: A[p..r] is sorted if pr then return -1 else if x q A [q] return binarySearch (A, q+1, r, x)