You don't say what field this is, but in a logic or math course this might be a perfectly fine sort of question if the objective is to recognize errors, incorrect statements, and poor reasoning.
Recognizing that something isn't true and saying why can be just as valuable as providing a proof of something that is true. After all, in the political sphere there is a lot of such flawed reasoning that you can see every day in common media.
So, before you object, or claim that the professors are incompetent, explore why this is happening. Just the fact that it recurs implies to me that it may well be intentional.
However, I would hope that instructors using such a technique give some sort of warning beforehand.
I used to warn my students that the final would have one question that would be extremely difficult (nearly impossible) for any of them to answer. It was a thought provoker. But I expected students to say "something intelligent" for such questions even though I didn't expect solutions. The grading has to reflect this, of course.