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.
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \mathcal{R}=\left\{\begin{array}{ccc}
(x_{1}, x_{1}) & (x_{1}, x_{2}) & (x_{2}, x_{2})\\ (x_{3}, x_{1}) & (x_{3}, x_{3}) & \end{array}
\right\}\\ \text{ sur } X=\{x_{1}, x_{2}, x_{3}\}\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\(
\xymatrix{
x_{1} && x_{2} \ar@(lu,ru)[]\ar@/^0.579pc/[dd]\ar@/^0.579pc/[lldd] \\
&&\\
x_{4} \ar@/^0.579pc/[rruu]\ar@/^0.579pc/[rr]\ar@(ld,rd)[] && x_{3} \ar@/^0.579pc/[uu]\ar@(ld,rd)[]\ar@/^0.579pc/[ll] \\
}
\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\(
\xymatrix{
x_{1} && x_{2} \ar@(lu,ru)[] \\
&&\\
&x_{3} \ar@(ld,rd)[]&
}
\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\(
\xymatrix{
x_{1} && x_{2} \ar@(lu,ru)[] \\
&&\\
&x_{3} \ar@(ld,rd)[]&
}
\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \mathcal{R}=\left\{\begin{array}{ccc}
(x_{1}, x_{1}) & (x_{1}, x_{4}) & (x_{2}, x_{2})\\ (x_{2}, x_{3}) & (x_{2}, x_{4}) & (x_{3}, x_{2})\\ (x_{3}, x_{4}) & \end{array}
\right\}\\ \text{ sur } X=\{x_{1}, x_{2}, x_{3}, x_{4}\}\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \mathcal{R}=\left\{\begin{array}{ccc}
(x_{1}, x_{1}) & (x_{2}, x_{2}) & (x_{4}, x_{4})\\ \end{array}
\right\}\\ \text{ sur } X=\{x_{1}, x_{2}, x_{3}, x_{4}\}\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\(
\xymatrix{
x_{1} \ar@(lu,ru)[]\ar@/^0.579pc/[rr] && x_{2} \ar@(lu,ru)[] \\
&&\\
x_{4} \ar@/^0.579pc/[rruu]\ar@/^0.579pc/[rr]\ar@(ld,rd)[] && x_{3} \ar@(ld,rd)[] \\
}
\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\(
\xymatrix{
x_{1} \ar@(lu,ru)[] && x_{2} \ar@(lu,ru)[] \\
&&\\
x_{4} \ar@(ld,rd)[] && x_{3} \ar@(ld,rd)[] \\
}
\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \xymatrix{x_{1} & x_{2} \ar@(ld,rd)[] & x_{3} \ar@(ld,rd)[] & x_{4} \ar@(ld,rd)[] & x_{5} \ar@(ld,rd)[]}\)
-
\(
\begin{array}{|c|}
\hline
S\\\hline
T\\\hline
A\\\hline
R\\\hline
\end{array}
\)
\( \xymatrix{x_{1} \ar@(ld,rd)[] \ar@/^1pc/[rr] & x_{2} \ar@(ld,rd)[] \ar@/^2pc/[rr] \ar@/^2.5pc/[rrr] & x_{3} \ar@/^3pc/[ll] \ar@(ld,rd)[] & x_{4} \ar@/^4pc/[ll] \ar@(ld,rd)[] \ar@/^5pc/[r] & x_{5} \ar@/^5.5pc/[lll] \ar@/^6pc/[l] \ar@(ld,rd)[]}\)
Cliquer ici pour afficher la solution
Exercice
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{red}{\not S}&\color{red}{\not T}&\color{green}{A}&\color{green}{R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{red}{\not A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{green}{A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{green}{A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{red}{\not S}&\color{red}{\not T}&\color{red}{\not A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{green}{A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{red}{\not S}&\color{green}{T}&\color{green}{A}&\color{green}{R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{green}{A}&\color{green}{R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{green}{A}&\color{red}{\not R}
\\\hline
\end{array}
\)
- \(
\begin{array}{|c|c|c|c|}
\hline
\color{green}{S}&\color{green}{T}&\color{red}{\not A}&\color{green}{R}
\\\hline
\end{array}
\)