L'exercice suivant est automatiquement et aléatoirement généré par ataraXy.
Si vous regénérez la page (F5) les valeurs seront changées.
La correction se trouve en bas de page.
Exercice
Quelles sont les propriétés satisfaites par les relations internes suivantes ? Aucune justification n'est attendue.
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \begin{array}{c||ccc} & x_{1} & x_{2} & x_{3} \\\hline\hline x_{1} & 0 & 0 & 0\\ x_{2} & 1 & 1 & 1\\ x_{3} & 1 & 1 & 0\end{array}\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\(
\xymatrix{
x_{1} \ar@/^0.79pc/[rr] && x_{2} \ar@/^0.79pc/[ll]\ar@(lu,ru)[] \\
&&\\
&x_{3} \ar@/^0.79pc/[luu]\ar@/^0.79pc/[ruu]\ar@(ld,rd)[]&
}
\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \xymatrix{x_{1} \ar@(ld,rd)[] \ar@/^1pc/[rrr] \ar@/^1.5pc/[rrrr] & x_{2} \ar@/^2pc/[r] & x_{3} \ar@/^2.5pc/[l] \ar@(ld,rd)[] & x_{4} \ar@/^3.5pc/[lll] \ar@/^4pc/[r] & x_{5} \ar@/^4.5pc/[llll] \ar@/^5pc/[l] \ar@(ld,rd)[]}\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \begin{array}{c||cccc} & x_{1} & x_{2} & x_{3} & x_{4} \\\hline\hline x_{1} & 1 & 0 & 0 & 0\\ x_{2} & 0 & 1 & 0 & 0\\ x_{3} & 0 & 0 & 1 & 0\\ x_{4} & 0 & 0 & 0 & 1\end{array}\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \begin{array}{c||ccc} & x_{1} & x_{2} & x_{3} \\\hline\hline x_{1} & 1 & 1 & 1\\ x_{2} & 0 & 1 & 0\\ x_{3} & 1 & 1 & 1\end{array}\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \begin{array}{c||ccccc} & x_{1} & x_{2} & x_{3} & x_{4} & x_{5} \\\hline\hline x_{1} & 0 & 0 & 1 & 0 & 0\\ x_{2} & 0 & 1 & 0 & 0 & 1\\ x_{3} & 1 & 0 & 1 & 0 & 0\\ x_{4} & 0 & 0 & 0 & 1 & 0\\ x_{5} & 0 & 1 & 0 & 0 & 1\end{array}\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \begin{array}{c||ccc} & x_{1} & x_{2} & x_{3} \\\hline\hline x_{1} & 1 & 0 & 1\\ x_{2} & 1 & 1 & 1\\ x_{3} & 0 & 0 & 1\end{array}\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\(
\xymatrix{
x_{1} && x_{2} \\
&&\\
x_{4} && x_{3} \ar@(ld,rd)[] \\
}
\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\(
\xymatrix{
x_{1} \ar@(lu,ru)[]\ar@/^0.79pc/[rdd] && x_{2} \\
&&\\
&x_{3} \ar@/^0.79pc/[luu]\ar@(ld,rd)[]&
}
\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\(
\xymatrix{
x_{1} \ar@(lu,ru)[]\ar@/^0.579pc/[rr] && x_{2} \ar@/^0.579pc/[ll]\ar@(lu,ru)[] \\
&&\\
x_{4} \ar@/^0.579pc/[rr]\ar@(ld,rd)[] && x_{3} \ar@(ld,rd)[]\ar@/^0.579pc/[ll] \\
}
\)
Cliquer ici pour afficher la solution
Exercice
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{red}{\not S}&\color{red}{\not T}&\color{red}{\not A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{red}{\not S}&\color{red}{\not T}&\color{red}{\not A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{red}{\not T}&\color{red}{\not A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{green}{A}&\color{green}{R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{red}{\not S}&\color{green}{T}&\color{red}{\not A}&\color{green}{R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{red}{\not T}&\color{red}{\not A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{red}{\not S}&\color{green}{T}&\color{green}{A}&\color{green}{R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{green}{A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{red}{\not A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{red}{\not A}&\color{green}{R}
\\\hline
\end{array}
\)