3. The International Standard Book Number (ISBN) is an example of an error detecting code. In this question we will use the version of ISBN that was in effect before 2007 (some small changes have occurred since then). Each book is assigned a unique 10 digit number, called the ISBN-10. The first 9 digits record information about the publisher, author, etc, and the 10th digit is a check digit d. The check vector is c = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1] and the check digit is such that if x is a valid ISBN-10 then c.x=0 in Z1. By convention, if the check digit is d = 10 then the symbol X is used to represent d for legibility. (a) Which of the following are valid ISBN-10 numbers? (Show your working) (i) 012012016X (ii) X908076010 (b) For how many values of a Z is 34a34X7258 a valid ISBN-10 number? (c) The ISBN-10 number 2572030951 is not valid. Given that an error has occurred in the 4th place from the left (and that no other errors have occurred), find the correct ISBN-10 number for this book.