Suppose that a five-digit code consists of four digits and a check digit assigned so that the sum of the five digits is divisible by 9. Assume that the digits 0 through 9 may be used in the first four digits of the code. When the sum of the first four digits is already divisible by 9, assume that 0 is always selected for the check digit. Determine whether the following errors would be detected and explain why they could or could not be detected.
a. The third and fourth digits have been transposed.
b. The third digit was supposed to be a 9 but was recorded as a 0.
c. The first digit is recorded as an 8 rather than a 3.
d. The check digit is recorded as a 9.
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