$\huge \forall x \, \exists y\, P(x, y)$ means that: > *"[[02 Areas/Math/Universal Quantifier|For All]] $x\in D_{0}$, there exists a value $y\in D_{1}$ such that $P(x, y)$ is [[Truth Value|True]]*. $\huge \exists x \, \forall y\, P(x, y)$ means that: > *"[[02 Areas/Math/Existential Quantifier|There Exists]] some $x\in D_{0}$ such that [[02 Areas/Math/Universal Quantifier|For All]] $y\in D_1$, $P(x, y)$ is [[02 Areas/Math/Truth Value|True]]"*.