Simplifying Quantified Statement For my assignment, I have to simplify this statement leaving no negations in the end.
$$\neg\exists x\ \forall x(\neg B(x) \wedge C(x))$$
Everything I've tried so far leaves me with a single negation sign on $B(x)$ or $C(x)$ and I just cannot figure this out. 

I assume that the negation on the very outside applies to the entire block.
What is the negation of a statement of the form $\exists x P(X)$? We should have $\forall x \neg P(x)$.
What is the negation of a statement of the form $\forall x Q(x)$? We should have $\exists x\neg Q(x)$.
Using these two rules, you can pass the negation all the way in towards the actual formula, and then use DeMorgan to finish the job. When you are left with a disjunction of two terms, you can combine them into an implication instead.
