\begin{frame}
  \frametitle{More Exam Preparation Tasks}

  \begin{alertgoal}{Exam Exercises}
    Try to derive yourself:
    \begin{itemize}
    \medskip
      \item $p \vee q,\;\; \neg p \;\;\vdash\;\; q$
    \medskip
      \item $p \to (q \to r) \;\;\vdash\;\; q \to (p \to r)$
    \medskip
      \item $(p \to q) \to r \;\;\vdash\;\; p \to (q \to r)$
    \medskip
      \item $p \vee (q \wedge r) \;\;\vdash\;\; p \vee q$
    \medskip
      \item $a \vee b,\;\; a \to c,\;\; \neg d \to \neg b \;\;\vdash\;\; c \vee d$
    \medskip
      \item $(a \to b) \wedge (b \to a) \;\;\vdash\;\; (a \wedge b) \vee (\neg a \wedge \neg b)$
    \medskip
      \item $a \wedge (b \vee c)  \;\;\vdash\;\; (a \wedge b) \vee (a \wedge c)$
    \medskip
      \item $\vdash\;\; ((p \to q) \to p) \to p$
    \medskip 
    \end{itemize}
  \end{alertgoal}  
\end{frame}