UPC code proof help i'm trying to prove the following problem..
1. Prove that if a single digit of a valid UPC is changed then the new code is not valid.

Answer - When the question asks to prove it, does it mean to litteraly do a mathematical problem where I prove that a UPC code is valid and then alter any digit and prove that that is not valid? (If so, that's really easy) On the other hand, does it want me to generalize the proof? 
2. If two digits are changed in a valid UPC, the new code may or may not be valid. Determine the type of changes to two digits that result in a valid code, and determine the change to two digits that result in a code that is not valid. Justify both of your answers.

Answer - For this problem, I need a direction to go about solving the problem rather than computing various mathematical checks. 
Thanks guys!

I believe part of the UPC code is a checksum-you could have told us that.  If so, you should be able to prove that changing any one digit makes the sum not check.  All the noncheck digits are interchangeable, and clearly changing the check digit causes it to fail.  For 2, you can just demonstrate one change of two digits that is valid and one change that is not.
