\begin{frame}[t] \frametitle{Quantifiers} \vspace{-1ex} Instead of `$x$ is green' we now want to say: \begin{itemize} \item `somebody is green', or \item `everybody is green'. \end{itemize} \pause \begin{goal}{Existential quantifier} \vspace{-1ex} \begin{talign} \myex{x}{\phi} \end{talign} \vspace{-3ex} means: there exists some $x$ such that the formula $\phi$ is true. \end{goal} \pause \begin{exampleblock}{} \begin{malign} \myex{x}{P(x)} \quad\quad\hint{(somebody is green)} \end{malign} \end{exampleblock} \pause \begin{goal}{Universal quantifier} \vspace{-1ex} \begin{talign} \myall{x}{\phi} \end{talign} \vspace{-3ex} means: for every $x$ the formula $\phi$ is true. \end{goal} \pause \begin{exampleblock}{} \begin{malign} \myall{x}{P(x)} \quad\quad\hint{(everybody is green)} \end{malign} \end{exampleblock} \vspace{10cm} \end{frame}