Bruce Schneier has a wonderful piece in his security blog. In it, he first describes some basic mathematical logic. Then he describes a psychological experiment developed in the 1960's, that reassures you (after you have stumbled through schneier's tutorial). The experiment demonstrates that the great majority of people (even if they have taken the logic class) have difficulty doing this type of logical reasoning.
Except when the logic is framed in terms of cheating. For some reason, the threat of cheating turns our logical brains on, and the majority of people do the exact same kind of mathematical logic effortlessly. In my opinion, the long paragraphs Schneier chose to write are intimidating, but please hang in there. It's a good read.