2.10 Negating Statements

Logic

Negating Statements

• These tie back to DeMorgan’s Laws

Example

$\sim (\forall x\in \mathbb{X},\mathbb{P}(x))=\exists x\in X,\sim \mathbb{P}(x)$ $\sim (\exists x\in X,\mathbb{P}(x))=\forall x\in \mathbb{X},\sim \mathbb{P}(x)$

• In words this would be: It is not the case that $\mathbb{P}(x)$ is true for all Natural Numbers $x$.