I have a quick question regarding the Set Theory. The task states:
Find out if, for any given set, is true: (A\B)∩(C\D)=∅
(it is a rough translation from my language so.. sorry for that but I hope it's OK in terms of mathematics in English)
The results say that the statement is true but I can't seem to find the proof. I've spent like the last couple of hours trying to get to the result in many different ways and to find it online but without any luck.
Therefore I would love to hear any suggestions. At the moment, it seems to me that it doesn't apply for any given set but that's just my opinion.
Thank you in advance.
UPDATE
So after several debates with my peers and a math teacher we came to the conclusion: I was meant to find just one solution to prove the statement (thus I didn't have to prove it for all possible sets), thus making it super easy actually. It was my misunderstanding of the task.
Anyway, thanks to all of you for your suggestions (and for the speed).
Finally, if there's any desperate Czech student facing the same problem, here's the original task (so that it can be easily found):
Zjistěte, zda pro libovolné množiny A, B, C, D platí (A\B)∩(C\D)=∅.
(Last note: If there's any Czech, or a person learning Czech, reading this - I know the translation might be slightly off but my math language understanding transfered into English is quite... well, there are some gaps)