Quantifier Negation Laws

$\neg \forall ,P(x)\equiv \exists x,\neg P(x)$ $\neg \exists ,P(x)\equiv \forall x,\neg P(X)$ Negate the predecates, and the quantifier

Negating Predicates with Negated Quantifiers

$\exists x\neg \forall y,C(y,x)$

1. Remove all negations in front of quantifiers
2. Flip quantifiers