\begin{frame} \frametitle{Exercise: For All \& Implication} \begin{goal}{} \begin{salign} \forall\,X\,(\varphi_1 \Rightarrow \varphi_2) \;\;\equiv\;\; &\neg\exists\,X\,(\varphi_1 \wedge \neg\varphi_2) \end{salign} \end{goal} \medskip The formula \logicquerya \pause is \emph{logically equivalent to} \logicqueryb \end{frame}