1595 lines
40 KiB
TeX
1595 lines
40 KiB
TeX
%Clause Contingente 01 - jc
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\begin{frame}
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\begin{figure}[h!]
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\centering
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\begin{tikzpicture}[
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start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
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|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
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|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
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|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
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|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
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|
\node[lettre] (5) {$x2$} ;
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|
\node[lettre] (3) {$\lnot x2$} ;
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\node[lettre] (6) {$x3$} ;
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\node[lettre] (4) {$\lnot x3$} ;
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|
\node[lettre] (7) {$x4$} ;
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\node[lettre] (2) {$\lnot x4$} ;
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\node[lettre] (8) {$x1$} ;
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\end{tikzpicture}
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\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
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\label{fig:clause-conting}
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\end{figure}
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\end{frame}
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%Clause Contingente 02 - jc
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\begin{frame}
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\begin{figure}[h!]
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\centering
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|
\begin{tikzpicture}[
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start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
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|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
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|
}
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|
]
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|
\node[lettre] (1) {$\lnot x1$} ;
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\node[lettre] (5) {$x2$} ;
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\node[lettre] (3) {$\lnot x2$} ;
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\node[lettre] (6) {$x3$} ;
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\node[lettre] (4) {$\lnot x3$} ;
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\node[lettre] (7) {$x4$} ;
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\node[lettre] (2) {$\lnot x4$} ;
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\node[lettre] (8) {$x1$} ;
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\draw[arr] (1) -- (5) ;
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\end{tikzpicture}
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\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
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\label{fig:clause-conting}
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\end{figure}
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\end{frame}
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%Clause Contingente 03 - jc
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\begin{frame}
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\begin{figure}[h!]
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|
\centering
|
|
\begin{tikzpicture}[
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|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
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|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
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\node[lettre] (5) {$x2$} ;
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|
\node[lettre] (3) {$\lnot x2$} ;
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|
\node[lettre] (6) {$x3$} ;
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|
\node[lettre] (4) {$\lnot x3$} ;
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\node[lettre] (7) {$x4$} ;
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\node[lettre] (2) {$\lnot x4$} ;
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\node[lettre] (8) {$x1$} ;
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|
|
|
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\draw[arr] (1) -- (5) ;
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\draw[arr] (3) -- (8) ;
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\end{tikzpicture}
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\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
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\label{fig:clause-conting}
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\end{figure}
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\end{frame}
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%Clause Contingente 04 - jc
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\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
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|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
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|
}
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|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
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\node[lettre] (3) {$\lnot x2$} ;
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\node[lettre] (6) {$x3$} ;
|
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\node[lettre] (4) {$\lnot x3$} ;
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\node[lettre] (7) {$x4$} ;
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\node[lettre] (2) {$\lnot x4$} ;
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\node[lettre] (8) {$x1$} ;
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\draw[arr] (1) -- (5) ;
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\draw[arr] (3) -- (8) ;
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\draw[arr] (4) -- (7) ;
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\end{tikzpicture}
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\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
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\label{fig:clause-conting}
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\end{figure}
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\end{frame}
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%Clause Contingente 05 - jc
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\begin{frame}
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|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
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start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
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\node[lettre] (5) {$x2$} ;
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\node[lettre] (3) {$\lnot x2$} ;
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\node[lettre] (6) {$x3$} ;
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\node[lettre] (4) {$\lnot x3$} ;
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\node[lettre] (7) {$x4$} ;
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\node[lettre] (2) {$\lnot x4$} ;
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\node[lettre] (8) {$x1$} ;
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\draw[arr] (1) -- (5) ;
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\draw[arr] (3) -- (8) ;
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\draw[arr] (2) -- (6) ;
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\draw[arr] (4) -- (7) ;
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\end{tikzpicture}
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\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
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\label{fig:clause-conting}
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\end{figure}
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\end{frame}
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%Clause Contingente 06 - jc
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\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
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\node[lettre] (3) {$\lnot x2$} ;
|
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\node[lettre] (6) {$x3$} ;
|
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\node[lettre] (4) {$\lnot x3$} ;
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\node[lettre] (7) {$x4$} ;
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\node[lettre] (2) {$\lnot x4$} ;
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\node[lettre] (8) {$x1$} ;
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\node[chiffre, above right of=1] {1} ;
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\draw[arr] (1) -- (5) ;
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\draw[arr] (3) -- (8) ;
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\draw[arr] (2) -- (6) ;
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\draw[arr] (4) -- (7) ;
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|
\end{tikzpicture}
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\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
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\label{fig:clause-conting}
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\end{figure}
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\end{frame}
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%Clause Contingente 07 - jc
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\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
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\node[lettre] (4) {$\lnot x3$} ;
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\node[lettre] (7) {$x4$} ;
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\node[lettre] (2) {$\lnot x4$} ;
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\node[lettre] (8) {$x1$} ;
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\node[chiffre, above right of=1] {1} ;
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\node[chiffre, above left of=2] {2} ;
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\draw[arr] (1) -- (5) ;
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\draw[arr] (3) -- (8) ;
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\draw[arr] (2) -- (6) ;
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|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
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|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
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|
\label{fig:clause-conting}
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|
\end{figure}
|
|
\end{frame}
|
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%Clause Contingente 08 - jc
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|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
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|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
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|
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|
\node[chiffre, above right of=1] {1} ;
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|
\node[chiffre, below right of=3] {3} ;
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|
\node[chiffre, above left of=2] {2} ;
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|
|
|
\draw[arr] (1) -- (5) ;
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|
\draw[arr] (3) -- (8) ;
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|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
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|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 09 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
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|
\node[lettre] (8) {$x1$} ;
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|
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|
\node[chiffre, above right of=1] {1} ;
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|
\node[chiffre, below right of=3] {3} ;
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|
\node[chiffre, below left of=4] {4} ;
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\node[chiffre, above left of=2] {2} ;
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|
|
|
\draw[arr] (1) -- (5) ;
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|
\draw[arr] (3) -- (8) ;
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|
\draw[arr] (2) -- (6) ;
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|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 10 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 11 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 12 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, below left of=7] {7} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 13 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, below left of=7] {7} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
\node[chiffre, above left of=8] {8} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 14 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[left of=8] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, below left of=7] {7} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
\node[chiffre, above left of=8] {8} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 15 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[right of=1] {\textcolor{red}{faux}} ;
|
|
\node[left of=8] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, below left of=7] {7} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
\node[chiffre, above left of=8] {8} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 16 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[right of=1] {\textcolor{red}{faux}} ;
|
|
\node[left of=7] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[left of=8] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, below left of=7] {7} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
\node[chiffre, above left of=8] {8} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 17 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[right of=1] {\textcolor{red}{faux}} ;
|
|
\node[left of=7] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[left of=2] {\textcolor{red}{faux}} ;
|
|
\node[left of=8] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, below left of=7] {7} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
\node[chiffre, above left of=8] {8} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 18 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[right of=1] {\textcolor{red}{faux}} ;
|
|
\node[right of=6] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[left of=7] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[left of=2] {\textcolor{red}{faux}} ;
|
|
\node[left of=8] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, below left of=7] {7} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
\node[chiffre, above left of=8] {8} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 19 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[right of=1] {\textcolor{red}{faux}} ;
|
|
\node[right of=6] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[left of=4] {\textcolor{red}{faux}} ;
|
|
\node[left of=7] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[left of=2] {\textcolor{red}{faux}} ;
|
|
\node[left of=8] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, below left of=7] {7} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
\node[chiffre, above left of=8] {8} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 20 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[right of=1] {\textcolor{red}{faux}} ;
|
|
\node[right of=5] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[right of=6] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[left of=4] {\textcolor{red}{faux}} ;
|
|
\node[left of=7] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[left of=2] {\textcolor{red}{faux}} ;
|
|
\node[left of=8] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, below left of=7] {7} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
\node[chiffre, above left of=8] {8} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Contingente 21 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-45+22.5+90:2.5)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (5) {$x2$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (6) {$x3$} ;
|
|
\node[lettre] (4) {$\lnot x3$} ;
|
|
\node[lettre] (7) {$x4$} ;
|
|
\node[lettre] (2) {$\lnot x4$} ;
|
|
\node[lettre] (8) {$x1$} ;
|
|
|
|
\node[right of=1] {\textcolor{red}{faux}} ;
|
|
\node[right of=5] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[right of=3] {\textcolor{red}{faux}} ;
|
|
\node[right of=6] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[left of=4] {\textcolor{red}{faux}} ;
|
|
\node[left of=7] {\textcolor{green!75!black}{vrai}} ;
|
|
\node[left of=2] {\textcolor{red}{faux}} ;
|
|
\node[left of=8] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, above right of=5] {5} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below right of=6] {6} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
\node[chiffre, below left of=7] {7} ;
|
|
\node[chiffre, above left of=2] {2} ;
|
|
\node[chiffre, above left of=8] {8} ;
|
|
|
|
\draw[arr] (1) -- (5) ;
|
|
\draw[arr] (3) -- (8) ;
|
|
\draw[arr] (2) -- (6) ;
|
|
\draw[arr] (4) -- (7) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause contingente : $(x_{1} \vee x_{2}) \wedge (x_{3} \vee x_{4})$}
|
|
\label{fig:clause-conting}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Valide 01 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Valide 02 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
%Clause Valide 03 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
%Clause Valide 04 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2)
|
|
(3) edge[loop below] (3) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
%Clause Valide 05 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2)
|
|
(3) edge[loop below] (3)
|
|
(4) edge[loop above] (4) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
%Clause Valide 06 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2)
|
|
(3) edge[loop below] (3)
|
|
(4) edge[loop above] (4) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
%Clause Valide 07 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, below right of=2] {2} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2)
|
|
(3) edge[loop below] (3)
|
|
(4) edge[loop above] (4) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
|
|
|
|
%Clause Valide 08 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, below right of=2] {2} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2)
|
|
(3) edge[loop below] (3)
|
|
(4) edge[loop above] (4) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
%Clause Valide 09 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, below right of=2] {2} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2)
|
|
(3) edge[loop below] (3)
|
|
(4) edge[loop above] (4) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
%Clause Valide 10 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\node[left of=4] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, below right of=2] {2} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2)
|
|
(3) edge[loop below] (3)
|
|
(4) edge[loop above] (4) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
%Clause Valide 11 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\node[right of=3] {\textcolor{red}{faux}} ;
|
|
\node[left of=4] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, below right of=2] {2} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2)
|
|
(3) edge[loop below] (3)
|
|
(4) edge[loop above] (4) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
%Clause Valide 12 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\node[right of=2] {\textcolor{green!75!black}{vrai}};
|
|
\node[right of=3] {\textcolor{red}{faux}} ;
|
|
\node[left of=4] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, below right of=2] {2} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2)
|
|
(3) edge[loop below] (3)
|
|
(4) edge[loop above] (4) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
|
|
%Clause Valide 13 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
start chain=circle placed {at=(\tikzchaincount*-90+180:1.6)},
|
|
lettre/.style={
|
|
on chain,
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
},
|
|
chiffre/.style={
|
|
node distance = 0.75cm
|
|
},
|
|
arr/.style={
|
|
->,
|
|
>=triangle 90
|
|
}
|
|
]
|
|
\node[lettre] (1) {$\lnot x1$} ;
|
|
\node[lettre] (2) {$x1$} ;
|
|
\node[lettre] (3) {$\lnot x2$} ;
|
|
\node[lettre] (4) {$x2$} ;
|
|
|
|
\node[right of=1] {\textcolor{red}{faux}} ;
|
|
\node[right of=2] {\textcolor{green!75!black}{vrai}};
|
|
\node[right of=3] {\textcolor{red}{faux}} ;
|
|
\node[left of=4] {\textcolor{green!75!black}{vrai}} ;
|
|
|
|
\node[chiffre, above right of=1] {1} ;
|
|
\node[chiffre, below right of=2] {2} ;
|
|
\node[chiffre, below right of=3] {3} ;
|
|
\node[chiffre, below left of=4] {4} ;
|
|
|
|
\path
|
|
(1) edge[loop above] (1)
|
|
(2) edge[loop above] (2)
|
|
(3) edge[loop below] (3)
|
|
(4) edge[loop above] (4) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause valide : $(x_{1} \vee \neg x_{1}) \wedge (x_{2} \vee \neg x_{2})$}
|
|
\label{fig:clause-valide}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
% clause insatisfiable 01 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
node distance=2.5cm,
|
|
lettre/.style={
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
}
|
|
]
|
|
\node[lettre] (nx1) {$\lnot x_1$} ;
|
|
\node[lettre, below of=nx1] (x1) {$x_1$} ;
|
|
\node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {};
|
|
\node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {};
|
|
\node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {};
|
|
\node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {};
|
|
|
|
\end{tikzpicture}
|
|
\caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$}
|
|
\label{fig:clause-insat}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
% clause insatisfiable 02 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
node distance=2.5cm,
|
|
lettre/.style={
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
}
|
|
]
|
|
\node[lettre] (nx1) {$\lnot x_1$} ;
|
|
\node[lettre, below of=nx1] (x1) {$x_1$} ;
|
|
\node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {};
|
|
\node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {};
|
|
\node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {};
|
|
\node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {};
|
|
\draw[->] (nx1l) -- (x1l);
|
|
|
|
\end{tikzpicture}
|
|
\caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$}
|
|
\label{fig:clause-insat}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
% clause insatisfiable 03 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
node distance=2.5cm,
|
|
lettre/.style={
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
}
|
|
]
|
|
\node[lettre] (nx1) {$\lnot x_1$} ;
|
|
\node[lettre, below of=nx1] (x1) {$x_1$} ;
|
|
\node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {};
|
|
\node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {};
|
|
\node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {};
|
|
\node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {};
|
|
\draw[->] (x1r) -- (nx1r);
|
|
\draw[->] (nx1l) -- (x1l);
|
|
\end{tikzpicture}
|
|
\caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$}
|
|
\label{fig:clause-insat}
|
|
\end{figure}
|
|
\end{frame}
|
|
|
|
% clause insatisfiable 04 - jc
|
|
\begin{frame}
|
|
\begin{figure}[h!]
|
|
\centering
|
|
\begin{tikzpicture}[
|
|
node distance=2.5cm,
|
|
lettre/.style={
|
|
draw,
|
|
circle,
|
|
minimum size=1cm
|
|
}
|
|
]
|
|
\node[lettre] (nx1) {$\lnot x_1$} ;
|
|
\node[lettre, below of=nx1] (x1) {$x_1$} ;
|
|
\node[coordinate,xshift=0.1cm] (x1r) at (x1.north) {};
|
|
\node[coordinate,xshift=-0.1cm] (x1l) at (x1.north) {};
|
|
\node[coordinate,xshift=0.1cm] (nx1r) at (nx1.south) {};
|
|
\node[coordinate,xshift=-0.1cm] (nx1l) at (nx1.south) {};
|
|
\draw[->] (x1r) -- (nx1r);
|
|
\draw[->] (nx1l) -- (x1l);
|
|
\path
|
|
(x1) edge[loop below] (x1)
|
|
(nx1) edge[loop above] (nx1) ;
|
|
\end{tikzpicture}
|
|
\caption{Clause insatisfiable : $(x_{1} \vee x_{1}) \wedge (\neg x_{1} \vee \neg x_{1})$}
|
|
\label{fig:clause-insat}
|
|
\end{figure}
|
|
\end{frame}
|