You could consider the domain to be a group of people and P(x,y) to mean "x knows y". Try to figure out, provided the first proposition is true, whether the second proposition is always true, is always false, or can be either.

Also, if is false, it means that is true. You can move the negation inside, i.e., put it in front of . Then it is easier to compare the two formulas. Moving negation inside is also useful in problem #2. (Edit: Disregard the following. Basically, it reduces to question whether implies . To answer it, it is important to know if the domain is empty.)