"The contrapositive of a conditional statement."

Who would have ever thought that statement could cause such chaos in people's brains? It's easy, and I didn't need the teacher to explain it, even, for it's written clearly in the book. Read and learn:

p-->q is the given conditional statement. You'd read it as "if p, then q".
~p-->~q is the inverse of that, and is read as "if not p, then not q". With me so far? This stuff is easy.
q-->p is the converse of the original statement, and means, "if q, then p". Yay, we're learning.
~q-->~p is the contrapositive of the conditional statement, and simply reads, "if not q, then not p".

But ohdeargod, slap a big word like contrapositive on that, and the whole world goes nuts.

Perhaps I should have signed up for a harder level of math.