Could anybody help me with the proof
I don't have my book with me at the moment (and I don't trust myself to do the full proof without it, no matter how elementary), so I won't do the whole thing, but think about this as an induction proof. De Morgan's Law holds for two sets. Can you think of a way to show that if it holds for N sets that it will also hold for N+1? (Given that it holds for 2 sets.)
Note: I'm having some thoughts about this for . I don't know if you might not run into trouble with that. But as your problem specifies an "n" as an upper index you should be fine for your proof.