2.1, due on September 2

There were a few difficult parts for me to understand. During the proof of theorem 2.2, I got lost during the second step when they used -bc+bc=0. But later after rereading it, I realized that it was just a trick they were using and not something derived from an earlier equation. The first part of the proof of corollary 2.4 where the book says they have nothing to prove if the sets are disjoint didn't make sense to me. I don't understand why that is not applicable to the corollary. I didn't understand the second half of the proof for corollary 2.5 when they begin to suppose some inequalities. I didn't know where they got the s and t and how they came up with the inequalities and the rest of the proof built off of those things.

All in all I really enjoyed section 2.1. I enjoyed congruence and congruence classes when I learned about them in 290, because ever since I was in elementary school my dad would try to explain them to me and it was mostly nonsense to me until I took 290. I think the most interesting part of the section is the ending which states the corollary in which the set of all congruence classes modulo n has exactly n elements. I didn't come to that conclusion as I was reading the chapter but once it told me, it was such a logical completion of the section and makes a lot of the chapter solidified in my mind. I also liked the proof for theorem 2.3 because it reminded me that congruence can be proven by proving reflexive, symmetric, and transitive properties.