2. 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 ifp>r then return -1 else q A[q] return binarySearch (A, p, q-1, x) return q return binarySearch ( A, q+1, r, x)