Choosing equivalent quantifier expressions

Question

Which of the following expressions are equivalent to $∃x∀y(P(x,y)∧¬Q(x,y))$

1. $¬∀x∃y(¬P(x,y)∨Q(x,y))$

2. $∃x∀y¬(¬P(x,y)∨Q(x,y))$

3. $∀x∃y(P(x,y)∨¬Q(x,y))$

4. $∃x∀y(¬P(x,y)∨Q(x,y))$

I chose 1 and 2. 1 due to the negation in front of the first universal quantifier symbol and 2 because of the negation in front of $(¬P(x,y)∨Q(x,y))$. Can someone verify my answers?

Answer 1

Yes, so far your answers are correct.

Your answer could be improved by arguing why 3. and 4. are not equivalent to the original formulation. You can do this by finding an example for $P$ and $Q$ such that the results of 3. and 1. or 3. and 4. differ.