ajout en vrac de tous les partiels

diff --git a/partiels/130311S2/main.aux b/partiels/130311S2/main.aux
new file mode 100644 (file)
index 0000000..d30543e
--- /dev/null
+++ b/partiels/130311S2/main.aux
@@ -0,0 +1,11 @@
+\relax 
+\catcode`:\active
+\catcode`;\active
+\catcode`!\active
+\catcode`?\active
+\select@language{french}
+\@writefile{toc}{\select@language{french}}
+\@writefile{lof}{\select@language{french}}
+\@writefile{lot}{\select@language{french}}
+\newlabel{item1}{{1}{2}}[None]
+\newlabel{item2}{{2}{2}}[None]

diff --git a/partiels/130311S2/main.log b/partiels/130311S2/main.log
new file mode 100644 (file)
index 0000000..6fdc401
--- /dev/null
+++ b/partiels/130311S2/main.log
@@ -0,0 +1,1173 @@
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diff --git a/partiels/131003S1/controle.pdf b/partiels/131003S1/controle.pdf
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diff --git a/partiels/131003S1/controle.tex b/partiels/131003S1/controle.tex
new file mode 100644 (file)
index 0000000..0435c0c
--- /dev/null
+++ b/partiels/131003S1/controle.tex
@@ -0,0 +1,101 @@
+\documentclass[11pt,a4paper,french]{article}
+\usepackage[francais]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage{a4}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{framed}
+\usepackage[amsmath,thmmarks,thref,framed]{ntheorem}
+\usepackage[dvips]{graphics}
+\usepackage{epsfig}
+\usepackage{calc}
+\usepackage{tabls}
+\usepackage{times}
+\usepackage{tabularx}
+\usepackage{textcomp}
+\usepackage{pst-all}
+\usepackage[a4paper]{geometry}
+
+\input{symboles.sty}
+\geometry{hmargin=1cm, vmargin=1.5cm}
+
+\title{
+DUT d'informatique. Contrôle de mathématiques discrètes.\\  
+Semestre 1 (Octobre 2013). Durée 1h.}
+
+\date{}
+
+\begin{document}
+\maketitle
+
+\noindent Seule une fiche manuscrite de format A5 est autorisée. 
+Tous les exercices de ce sujet sont indépendants les uns des autres. 
+Dans tout ce qui suit, on considère une algèbre de Boole
+munie des opérateurs classiques ``+'', ``.'', 
+``$\overline{\begin{array}{l}~\end{array}}$'' et des variables booléennes 
+$a$, $b$, $c$, $d$.
+
+
+\section{Cours}
+
+\begin{enumerate}
+\item La première règle de suppression de la redondance est: ``dans une somme booléenne, tout terme absorbe ses  multiples''.   Démontrer cette règle (sans se servir des règles de suppression de redondance naturellement).
+\item Donner la définition de \og la forme cannonique disjonctive d'une expression\fg{}.
+\item Démontrer qu'il y a  1024 mintermes à 10 variables. 
+Si vous utilisez un théorème pour faire la preuve, il faudra le prouver.
+\item Que dire des colonnes adjacentes d'une table de Karnaugh? Et les lignes ?
+
+\end{enumerate}
+
+
+
+
+\section{Forme canonique disjonctive}
+Donner la forme canonique disjonctive de l'expression suivante en détaillant les calculs:
+$$
+(a + b + \overline{c}).\overline{(\overline{a} + bc)}.
+$$
+
+\section{Table de Karnaugh}
+On considère les deux expressions booléennes $E_1$ et $E_2$ suivantes:
+
+$$
+\begin{array}{rcl}
+E_1 &= &\overline{a}.\overline{b} + a.c+ a.\overline{b}.\overline{c},\\
+E_2 &=& a.\overline{b} + a.c.d + a.b.c +\overline{a}.\overline{b}.\overline{c}.
+\end{array}
+$$
+
+\begin{enumerate}
+\item A l'aide d'une table de Karnaugh donner l'expression $K_1$ qui 
+  serait la forme la plus réduite de $E_1$. 
+
+\item A l'aide d'une autre table de Karnaugh donner l'expression 
+  $K_2$ qui serait la forme la plus réduite de $E_2$.
+
+\item  Justifier algébriquement que l'on a l'égalité $E_1 = K_1$.
+
+\item Justifier algébriquement que l'on a l'égalité $E_2 = K_2$.
+\end{enumerate}
+
+\section{Opérateur de Peirce}
+On considère l'opérateur binaire de Peirce 
+défini pour toute paire de variables booléennes $(a,b)$ par 
+$$
+a \downarrow b = \overline{a}.\overline{b}
+$$.
+
+\begin{enumerate}
+\item Que valent  
+$a \downarrow 0$ puis $0 \downarrow 0$ et enfin   $1 \downarrow 1$?
+\item Que valent $(a \downarrow 0) \downarrow (b \downarrow 0)$ et
+ $(a \downarrow b ) \downarrow 0$ ?
+\item Réécrire l'expression  $\overline{a}.(b+c)$ sans utiliser 
+les opérateurs ``+'', ``.'' et 
+``$\overline{\begin{array}{l}~\end{array}}$'' mais en
+n'utilisant que l'opérateur de Peirce et des parenthèses.
+\item L'opérateur de Peirce est-il associatif? Le prouver.
+\end{enumerate}
+
+\end{document}

diff --git a/partiels/131003S1/controle.tex.bak b/partiels/131003S1/controle.tex.bak
new file mode 100644 (file)
index 0000000..97e056d
--- /dev/null
+++ b/partiels/131003S1/controle.tex.bak
@@ -0,0 +1,102 @@
+\documentclass[11pt,a4paper,french]{article}
+\usepackage[francais]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage{a4}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{framed}
+\usepackage[amsmath,thmmarks,thref,framed]{ntheorem}
+\usepackage[dvips]{graphics}
+\usepackage{epsfig}
+\usepackage{calc}
+\usepackage{tabls}
+\usepackage{times}
+\usepackage{tabularx}
+\usepackage{textcomp}
+\usepackage{pst-all}
+\usepackage[a4paper]{geometry}
+
+\input{symboles.sty}
+\geometry{hmargin=1cm, vmargin=1.5cm}
+
+\title{
+DUT d'informatique. Contrôle de mathématiques discrètes.\\  
+Semestre 1 (Octobre 2013). Durée 1h\\ 
+}
+
+\date{}
+
+\begin{document}
+\maketitle
+
+\noindent Seule une fiche manuscrite de format A5 est autorisée. 
+Tous les exercices de ce sujet sont indépendants les uns des autres. 
+Dans tout ce qui suit, on considère une algèbre de Boole
+munie des opérateurs classiques ``+'', ``.'', 
+``$\overline{\begin{array}{l}~\end{array}}$'' et des variables booléennes 
+$a$, $b$, $c$, $d$\ldots
+
+
+\section{Cours}
+
+\begin{enumerate}
+\item La première règle de suppression de la redondance est: ``Dans une somme booléenne, tout terme absorbe ses  multiples: $a + a.b = a$.''.   Démontrer cette règles (sans se servir des règles de suppression de redondance naturellement).
+\item Donner la définition de \og la forme cannonique disjonctive d'une expression\fg{}.
+\item Démontrer qu'il y a  1024 mintermes à 10 variables. 
+Si vous utilisez un théorème pour faire la preuve, il faudra le prouver.
+\item Que dire des colonnes adjacentes d'une table de Karnaugh? Et les lignes ?
+
+\end{enumerate}
+
+
+
+
+\section{Forme canonique disjonctive}
+Donner la forme canonique disjonctive de l'expression suivante en détaillant les calculs:
+$$
+(a + b + \overline{c}).\overline{(\overline{a} + bc)}.
+$$
+
+\section{Table de Karnaugh}
+On considère les deux expressions booléennes $E_1$ et $E_2$ suivantes:
+
+$$
+\begin{array}{rcl}
+E_1 &= &\overline{a}.\overline{b} + a.c+ a.\overline{b}.\overline{c},\\
+E_2 &=& a.\overline{b} + a.c.d + a.b.c +\overline{a}.\overline{b}.\overline{c}.
+\end{array}
+$$
+
+\begin{enumerate}
+\item A l'aide d'une table de Karnaugh donner l'expression $K_1$ qui 
+  serait la forme la plus réduite de $E_1$. 
+
+\item A l'aide d'une autre table de Karnaugh donner l'expression 
+  $K_2$ qui serait la forme la plus réduite de $E_2$.
+
+\item  Justifier algébriquement que l'on a l'égalité $E_1 = K_1$.
+
+\item Justifier algébriquement que l'on a l'égalité $E_2 = K_2$.
+\end{enumerate}
+
+\section{Opérateur de Peirce}
+On condidère l'opérateur binaire de Peirce 
+défini pour toute paire de variables booléenne $(a,b)$ par 
+$$
+a \downarrow b = \overline{a}.\overline{b}
+$$.
+
+\begin{enumerate}
+\item Que valent  
+$a \downarrow 0$ puis $0 \downarrow 0$ et enfin   $1 \downarrow 1$?
+\item Que valent $(a \downarrow 0) \downarrow (b \downarrow 0)$ et
+ $(a \downarrow b ) \downarrow 0$ ?
+\item Réécrire l'expression  $\overline{a}.(b+c)$ sans utiliser 
+les opérateurs ``+'', ``.'' et 
+``$\overline{\begin{array}{l}~\end{array}}$'' mais en
+n'utilisant que l'opérateur de Peirce et des parenthèses.
+\item L'opéreteur de Peirce est-il associatif? Le prouver.
+\end{enumerate}
+
+\end{document}

diff --git a/partiels/131003S1/controle.tex~ b/partiels/131003S1/controle.tex~
new file mode 100644 (file)
index 0000000..7c54d59
--- /dev/null
+++ b/partiels/131003S1/controle.tex~
@@ -0,0 +1,102 @@
+\documentclass[11pt,a4paper,french]{article}
+\usepackage[francais]{babel}
+\usepackage[utf8]{inputenc}
+\usepackage{a4}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{framed}
+\usepackage[amsmath,thmmarks,thref,framed]{ntheorem}
+\usepackage[dvips]{graphics}
+\usepackage{epsfig}
+\usepackage{calc}
+\usepackage{tabls}
+\usepackage{times}
+\usepackage{tabularx}
+\usepackage{textcomp}
+\usepackage{pst-all}
+\usepackage[a4paper]{geometry}
+
+\input{symboles.sty}
+\geometry{hmargin=1cm, vmargin=1.5cm}
+
+\title{
+DUT d'informatique. Contrôle de mathématiques discrètes.\\  
+Semestre 1 (Octobre 2013). Durée 1h\\ 
+}
+
+\date{}
+
+\begin{document}
+\maketitle
+
+\noindent Seule une fiche manuscrite de format A5 est autorisée. 
+Tous les exercices de ce sujet sont indépendants les uns des autres. 
+Dans tout ce qui suit, on considère une algèbre de Boole
+munie des opérateurs classiques ``+'', ``.'', 
+``$\overline{\begin{array}{l}~\end{array}}$'' et des variables booléennes 
+$a$, $b$, $c$, $d$\ldots
+
+
+\section{Cours}
+
+\begin{enumerate}
+\item La première règle de suppression de la redondance est: ``Dans une somme booléenne, tout terme absorbe ses  multiples: $a + a.b = a$.''.   Démontrer cette règles (sans se servir des règles de suppression de redondance naturellement).
+\item Donner la définition de \og la forme cannonique disjonctive d'une expression\fg{}.
+\item Démontrer qu'il y a  1024 mintermes à 10 variables. 
+Si vous utilisez un théorème pour faire la preuve, il faudra le prouver.
+\item Que dire des colonnes adjacentes d'une table de Karnaugh? Et les lignes ?
+
+\end{enumerate}
+
+
+
+
+\section{Forme canonique disjonctive}
+Donner la forme canonique disjonctive de l'expression suivante en détaillant les calculs:
+$$
+(a + b + \overline{c}).\overline{(\overline{a} + bc)}.
+$$
+
+\section{Table de Karnaugh}
+On considère les deux expressions booléennes $E_1$ et $E_2$ suivantes:
+
+$$
+\begin{array}{rcl}
+E_1 &= &\overline{a}.\overline{b} + a.c+ a.\overline{b}.\overline{c},\\
+E_2 &=& a.\overline{b} + a.c.d + a.b.c +\overline{a}.\overline{b}.\overline{c}.
+\end{array}
+$$
+
+\begin{enumerate}
+\item A l'aide d'une table de Karnaugh donner l'expression $K_1$ qui 
+  serait la forme la plus réduite de $E_1$. 
+
+\item A l'aide d'une autre table de Karnaugh donner l'expression 
+  $K_2$ qui serait la forme la plus réduite de $E_2$.
+
+\item  Justifier algébriquement que l'on a l'égalité $E_1 = K_1$.
+
+\item Justifier algébriquement que l'on a l'égalité $E_2 = K_2$.
+\end{enumerate}
+
+\section{Opérateur de Peirce}
+On considère l'opérateur binaire de Peirce 
+défini pour toute paire de variables booléenne $(a,b)$ par 
+$$
+a \downarrow b = \overline{a}.\overline{b}
+$$.
+
+\begin{enumerate}
+\item Que valent  
+$a \downarrow 0$ puis $0 \downarrow 0$ et enfin   $1 \downarrow 1$?
+\item Que valent $(a \downarrow 0) \downarrow (b \downarrow 0)$ et
+ $(a \downarrow b ) \downarrow 0$ ?
+\item Réécrire l'expression  $\overline{a}.(b+c)$ sans utiliser 
+les opérateurs ``+'', ``.'' et 
+``$\overline{\begin{array}{l}~\end{array}}$'' mais en
+n'utilisant que l'opérateur de Peirce et des parenthèses.
+\item L'opérateur de Peirce est-il associatif? Le prouver.
+\end{enumerate}
+
+\end{document}

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