The Wason Selection Task (described by Pete Clark here) is a great problem for getting students to grapple with all of the intricacies of logical implication.
I will be teaching a discrete mathematics course for the first time in about a month, and I would love to have a sizable repository of similar questions.
Does anyone have a link to a big list of similar questions? If not, I am happy to hear your ideas about similar problems which might stimulate a similar amount of thinking about the other logical operators.