How to solve Nested Quantifiers problems-- Discrete Mathematics

Nested quantifiers are quantifiers that occur within the scope of other quantifiers. Example: ∀x∃yP(x, y) Quantifier order matters! To negate a sequence of nested quantifiers, you flip each quantifier in the sequence and then negate the predicate. So the negation of ∀x ∃y : P(x, y) is ∃x ∀y : P(x, y) and So the negation of ∃x ∀y : P(x, y) and ∀x ∃y : P(x, y).