The Universal [[Quantifier]] is a [[Quantifier]] denoting whether all values in some [[Domain]] $x\in D$ satisfy some [[Predicate|Predicate Function]] $P(x)$. The notation is denoted as: $\huge \begin{align} \forall x\,P(x)&, x\in D \end{align} $ Read as "for all $x$ $P(x)quot;. >[!example] Let P(x)$ be the [[Proposition|Statement]] $x^2 > 0$ > >$\forall x \,P(x)$ is [[Truth Value|False]] on the domain of $x\in \R$. > >$\forall x \,P(x)$ is [[Truth Value|True]] on the domain of $x\in \R^{-}$. It is usually assumed the [[Domain]] is nonempty, however if $\lvert D \rvert=0$, then the [[Universal Quantifier]] of the [[Predicate|Predicate Function]] on all $x \in D$ is always [[Truth Value|true]]. $\huge \begin{align} x &\in D\\ \lvert D \rvert = 0 &\implies \forall x\,P(x) \end{align}$