a) Prove that if a transposition error is made in the fourth and fifth entries of the ISBN-10 [0, 6, 7, 9, 7, 6, 2, 9, 0, 6], the error will be detected.
b) Prove that if a transposition error is made in any two adjacent entries of the ISBN-10 in part (a), the error will be detected.
c) Prove, in general, that the ISBN-10 code will always detect a transposition error involving two adjacent entries.