4. The check digit for ISBNs is one of the numbers 0, 1, 2, . .. , 9, or the letter X. One of the your fellow students comments”Gee, it sure is a pain to have to use that X all time. Why don’tthey just compute the check digit sum modulo 10 instead of modulo11, so that we can get rid of the X?” Would this plan work? Proveyour answer.
Assume that all ISBNs are 10 digits with the tenth digit thecheck digit. I know that using modulo 10 to compute the check digitwill catch single digit errors, but it will not always catch errorsregarding transposition of numbers in the ISBN. I am having adifficult time proving that the transposition errors will notalways be caught.
