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\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}