I have a question about the contrapositives... How can you assume that because (C and D) implies (not E), E implies ((not D) or (not C))? How do you know that (C and (not D)) doesn't imply (not E)? Just because (C and D) implies (not E), couldn't it be that just C implies (not E) regardless of whether it's combined with D or (not D)? In which case, how can you be sure that E implies ((not D) or (not C))? Or what if (not E) was a constant, and every combination implied (not E), and (D and C) was just one of those combinations? I'm probably totally wrong in questioning this, since you know much more about this sorta stuff than me, but oh well. At least I'll find out what's wrong with my question.