Given the statement $\forall z \in C, \forall y \in R, \exists x \in R, (z=x+y)$, what are the steps one should take to negate the statement?
The negation I arrived at is $\exists (z \in C, y \in R), \forall x \in R, (z \neq x + y)$. However, I'm unsure 1) if this actually correct, and 2) how I'd actually show mathematically that this is correct (if it is).
My method for negating statements is essentially to just stare at it and go off of intuition, which is obviously not the "formal" method. So what kind of steps should one follow to properly negate a general statement? Or there any laws of negation that one can follow when there's several quantifiers like this?