2.2, due January 12

1. Difficult: I'm a little confused. It seems like the book is contradicting itself. It asks at the beginning of the section if [a] + [c] = [a + c] and it gave some examples that worked. But then it later gave an example where 1+7=8 (or B+C=D) and then -3+25=12 (or B+C=A) thus this obviously doesn't work. But then it gives the definition which states "Addition and multiplication in Zn are defined by [a]+[c]=[a+c] and [a]*[c]=[a*c]. What did I miss? I feel like they just barely said this did NOT work, but now they are putting it in a definition so it obviously DOES. I've analyzed the theorem that comes between the two statements, but it doesn't seem to help me segue between the two ideas. And now I'm just really confused.
2. Reflective: Even though I don't really understand the property as mentioned above, I do like that it seems to follow all of the basic arithmetic rules. It's commutative, associative, distributive. This will make it a lot easier for me in the future.