\begin{frame} \frametitle{Valuations} \begin{goal}{} An \emph{assignment of truth values} to variables is a \emph{valuation}. \end{goal} \pause {\small (In the book, for predicate logic, also called look-up function)} \pause \begin{exampleblock}{} The valuation $\svaluation$ on the previous slide is \begin{talign} \valuation{p} = \T && \valuation{q} = \T && \valuation{r} = \F \end{talign} \pause The truth value of $p \vee \neg q \to r$ with this valuation is \pause $\F$. \end{exampleblock} \begin{itemize} \pause \item A valuation corresponds to one line in the truth table. \pause \item A truth table systemically considers all possible valuations. \end{itemize} \pause \begin{exampleblock}{} For \quad $p \vee \neg q \to r$, \quad there are $8 = 2^3$ valuations. \end{exampleblock} \end{frame}