I'm getting an alert from the script that says my question appears to be subjective, but I don't think it is. What I seek is an explanation as to what the statement in the title in quotes means. It asked me to do this for a specific statement in predicate logic, but I couldn't find a way to type out some of the symbols, which i am researching on my own right now.
Any help is appreciated, as I have a test on material like this tomorrow morning.
Presumably, it means that you should simplify $$\neg \forall x[P(x)]$$ to the equivalent $$\exists x[\neg P(x)]$$ and to simplify $$\neg \exists x[P(x)]$$ to $$\forall x[\neg P(x)].$$ A "quantifier in the scope of a negation" would be when the negated stated includes a quantifier and they can always be eliminated by the two above simplifications.