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FGI2: 4.3.2 und 4.4 verbessert

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Jim Martens
2014-11-06 17:03:11 +01:00
parent 3e7ecc520e
commit da5357f5fd
1 changed files with 9 additions and 6 deletions
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15
fgi2/Blatt4/Aufgabenblatt4.tex
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@ -49,23 +49,26 @@
SS(M) = 1(3(5763)^{*}1 + 1)^{\omega} SS(M) = 1(3(5763)^{*}1 + 1)^{\omega}
\] \]
\subsection{} \subsection{}
\[ \begin{alignat*}{2}
ES(M) = 1(3(5763)^{*}1 + 1)^{\omega} E_{S}(M) &=& E_{S}(1(3(5763)^{*}1 + 1)^{\omega}) \\
\] &=& (E_{S}(1)(E_{S}(3)(E_{S}(5)E_{S}(7)E_{S}(6)E_{S}(3))))^{\omega}
\subsection{} \end{alignat*}
\subsection{} %
\begin{alignat*}{2} \begin{alignat*}{2}
Sat(Teig \vee \lnot Hitze) &=& \{1, 4, 5\} \\ Sat(Teig \vee \lnot Hitze) &=& \{1, 4, 5\} \\
Sat(\lnot Teig) &=& \{1, 2, 3, 6, 7\} Sat(\lnot Teig) &=& \{1, 2, 3, 6, 7\}
\end{alignat*} \end{alignat*}
\subsection{} %Gegenbeispiel finden
\section{} %4.4 \section{} %4.4
\begin{tabular}{l|l|l} \begin{tabular}{l|l|l}
\(f\) & \(M_{kuchen} \models f \) & \(M_{kuchen}, \pi \models f\)\\ \(f\) & \(M_{kuchen} \models f \) & \(M_{kuchen}, \pi \models f\)\\
\hline \hline
\(\lozenge \square(\lnot Teig \vee Hitze) \)& nein & nein \\ \(\lozenge \square(\lnot Teig \vee Hitze) \)& nein & ja \\
\(\square \lozenge(\lnot Teig \vee Hitze)\) & ja & ja \\ \(\square \lozenge(\lnot Teig \vee Hitze)\) & ja & ja \\
\(\square (Hitze \;\mathcal{U}\; Backen)\) & nein & nein \\ \(\square (Hitze \;\mathcal{U}\; Backen)\) & nein & nein \\
\(\square \lozenge (Hitze \Rightarrow XX\lnot Backen)\) & ja & nein \\ \(\square \lozenge (Backen \Rightarrow XX\lnot Backen)\) & ja & ja \\
\(\square ((Hitze \wedge Teig) \Rightarrow \lozenge \lnot Teig)\) & ja & ja \\ \(\square ((Hitze \wedge Teig) \Rightarrow \lozenge \lnot Teig)\) & ja & ja \\
\(XX \lozenge (\lnot Hitze \wedge \lnot Teig)\) & nein & nein \(XX \lozenge (\lnot Hitze \wedge \lnot Teig)\) & nein & nein
\end{tabular} \end{tabular}