Originally Posted by

**emakarov** I rewrote the formula a bit to better show the scopes.

$\displaystyle \exists x\,\forall y \Big( Q(x,y) \wedge \big( [ \neg P(x,q) \vee Q(x,y)] \rightarrow Qy\big)\Big)$

I think your answer is correct. What is strange is that in the original formula two different predicates Q(x,y) and Q(y) are denoted by the same letter. My guess is that the person who assigned this wanted to say that only atomic formulas can be negated, and, seeing only P and Q, he/she said that negations can only be in front of P(x,y) and Q(x,y)