The [[02 Areas/Math/Logical Negation|Logical Negation]] of *"$P(x)$ is [[Truth Value|True]] [[02 Areas/Math/Universal Quantifier|For All]] $x \in Dquot;* is [[Equivalent]] to *"There [[02 Areas/Math/Existential Quantifier|Exists]] a value $x \in D$ that does [[02 Areas/Math/Logical Negation|Not]] satisfy $P(x)$."* $\huge \neg \forall x \, P(x) \equiv \exists x \,\neg P(x) $ The [[02 Areas/Math/Logical Negation|Logical Negation]] of *"[[02 Areas/Math/Existential Quantifier|There Exists]] a value $x\in D$ that satisfies the [[02 Areas/Math/Predicate|Predicate]] $P(x)quot;* is [[Equivalent]] to saying *"$x$ does [[Logical Negation|Not]] satisfy the [[02 Areas/Math/Predicate|Predicate]] $P(x)$ [[02 Areas/Math/Universal Quantifier|For All]] $x\in Dquot;*. $ \huge \neg \exists x \, P(x) \equiv \forall x\, \neg P(x) $ >[!quote] Every Day I am Shuffling, but what if there is one day I am not. - [[../Digipen/Alexander Young|Alexander Young]]