"“ X ∧ ¬ Y ∧ ¬ ( Z ⇒ Q ) .” And since I’m the professor, you can assume I’m correct about this. From this information alone, can you determine a unique set of values for the four variables? Or is there more than one possibility for them? There is actually only one solution. Here’s one way to tell. We know that X must be true, since it’s being “and-ed” in to another expression. We know that Y must be false, since its opposite is similarly being “and-ed” in. Finally, we also know that Z must be true and Q must be false, since the only way an implication ( ⇒ ) can be false is if its premise is true and its conclusion is false. And the implication here must be false if the professor is telling the truth, because its opposite is being “and-ed” in to the three other things. So the one and only answer is: X = 1 , Y = 0 , Z = 1 , Q = 0 . (You can figure this all out with truth tables too, of course, and for most examples you would. I just wanted to make an exercise that you could figure out in your head without pencil and paper.)"