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\def\thesection{4.\arabic{section})}
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\begin{document}
\author{Benjamin Kuffel, Jim Martens\\Gruppe 6}
\title{Hausaufgaben zum 10. November}
\maketitle

\setcounter{section}{2}
\section{} %4.3
	\subsection{}
	\begin{alignat*}{2}
		L(TS_{kuchen\_teil}) &=& (v(htwb^{*}k)^{*}o + r)^{*} \\
		L^{\omega}(TS_{kuchen\_teil}) &=& (v(htwb^{*}k)^{*}o + r)^{\omega}
	\end{alignat*}
	\subsection{}
	\[
		SS(M) = 1(3(5763)^{*}1 + 1)^{\omega}
	\]
	\subsection{}
	\[
		ES(M) = 1(3(5763)^{*}1 + 1)^{\omega}
	\]
	\subsection{}
	\begin{alignat*}{2}
		Sat(Teig \vee \lnot Hitze) &=& \{1, 4, 5\} \\
		Sat(\lnot Teig) &=& \{1, 2, 3, 6, 7\}
	\end{alignat*}	
	
\section{} %4.4
	\begin{tabular}{l|l|l}
		\(f\) & \(M_{kuchen} \models f \) & \(M_{kuchen}, \pi \models f\)\\
		\hline
		\(\lozenge \square(\lnot Teig \vee Hitze) \)& nein & nein \\
		\(\square	\lozenge(\lnot Teig \vee Hitze)\) & ja & ja \\
		\(\square	(Hitze \;\mathcal{U}\; Backen)\) & nein & nein \\
		\(\square	\lozenge (Hitze \Rightarrow XX\lnot Backen)\) & ja & nein \\
		\(\square ((Hitze \wedge Teig) \Rightarrow \lozenge \lnot Teig)\) & ja & ja \\
		\(XX \lozenge (\lnot Hitze \wedge \lnot Teig)\) & nein & nein  
	\end{tabular}
\end{document}