pg 48 - end of 3.1, due January 21

So, this last little bit of Seciton 3.1 wasn't all that bad.  The first example was a little confusing when I read throguh it the first time because I forgot what a Cartesian product was.  For some reason it came into my mind that a + a' was adding a congruence class and an integer together and I was baffled.  Then the lightbulb went off and I remembered what a Cartesian product was.  Everything else made sense after that.  I noitced how in our lecture on Wednesday we used Theorem 3.2 when proving or disproving that certain subsets of the integers were rings.  Reading the theorem made that process a little more clear.  In class I thought we were only allowed to do that in special cases, but here it says that we can do it for all cases where S is a subset of the ring R. That's wonderful news!