\begin{enumerate}
    \item $f:$ \quad Today it will be foggy.\\
          $r:$ \quad Today it will be rainy.
          $$ (f \land \neg r) \lor (\neg f \land r) $$
    \item $P:$ \quad For any program we can prove that the program halts.
          $$ P $$
    \item $s:$ \quad The system will never crash. \\
          $v:$ \quad The system has been verified during design time.\\
          $m:$ \quad The system is being monitored during runtime.
          $$ v \land m \imp s $$
\end{enumerate}