I was just wanting to make sure I had treated everything correctly when negating this statement. I wasn't 100% on how to treat the bracket between the existential quantifiers and whether or not I should change the predicates inside the brackets.

Negate:

First of all am I correct in thinking it reads "There exists an x that is an integer such that there exists a y that is an integer such that blah blah implies blah"?

My negation:

How do I determine which statements are true/false. I see it all as one statement is the problem how do I separate them?

Thanks.