\documentclass[12pt]{article}
\usepackage{ammaths}

\begin{document}

\module{Sets and relations}{1}{AP06}{55 mins}

%\prereq{}

\object{\begin{itemize}
        \item Introduce the concept of sets and relations.
        \item Introduce the main operations on sets : union, intersection and complement.
        \item Introduce the symbols $\in$, $\not\in$, $\subset$, $\not\subset$, $\cup$, $\cap$.
        \item Use of Venn diagram
	\end{itemize}}

\mater{\begin{itemize}
	\item 1 copy per student of the exercise sheet.
	\item Slideshow.
	\end{itemize}}

\modpart{Definitions}{10 mins}

Using a slideshow, the teacher introduce the main concepts. 

\modpart{Exercises}{remaining time}

A exercise sheet is handet out to the students.



\pagebreak
\moddocdis{Sets and relations}{1}{AP06}{55 mins}

\sectionblack{Sets and memberships}

\begin{enumerate}
\item Let $\Omega$ be an universe, $A$ and $B$ two subsets of $\Omega$. Describe $\bar{A}$, $A\cap B$ and $A\cup B$ when : 
      \begin{enumerate}
      \item $\Omega=\{1;2;3;4;5;6\} ; A=\{1;5;6\}$ and $B=\{2;5\}$.
      \item $\Omega$=\{blue;white;red;yellow\} ; $A=$\{blue;yellow\} and $B=$\{red\}.
      \item $\Omega=\{a;b;c;d;e;f;g\} ; A=\{a;b;f;g;e\}$ and $B=\{b;c;d\}$.
      \end{enumerate}
\item Let $A=\{b;r;a;v;o\}$ and $B=\{t;r;i;o\}$.\\
      Fill out the blanks with the symbols $=,\in,\not\in,\subset,\not\subset$ :\vspace{-10pt}
      \begin{multicols}{2}
      \begin{enumerate}
      \item $a \dots A$
      \item $\{t;r;a\} \dots B $
      \item $r \dots A\cap B$
      \item $\{r;i\} \dots A\cap B $
      \item $\{r;i\} \dots A\cap B $
      \item $\{s\} \dots A\cup B $
      \item $\{b;r;a;v;o\} \dots A\cup B $
      \item $i \dots A\cap B$
      \item $\{b;a;t;i;v;o;r\} \dots A\cup B $
      \end{enumerate}
      \end{multicols}
\item We pick out randomly a card in a 52 playing cards deck. Consider the events : \vspace{-10pt}
      \begin{multicols}{2}
      \begin{itemize}
      \item $A$ :~\og~Picking an ace~\fg~;
      \item $K$ :~\og~Picking an king~\fg~;
      \item $D$ :~\og~Picking an diamond~\fg~;
      \item $B$ :~\og~Picking an black card~\fg~;
      \item $F$ :~\og~Picking an figure (jack, queen or king)~\fg~;
      \end{itemize}
      \end{multicols}
      Give the probability of the events : \vspace{-10pt}
      \begin{enumerate}
      \begin{multicols}{4}
      \item $A$ ;
      \item $K$ ;
      \item $D$ ;
      \item $B$ ;
      \item $F$ ;
      \item $A\cap D$ ;
      \item $A\cap B$ ;
      \item $B\cap F$ ;
      \item $A\cup D$ ;
      \item $A\cup B$ ;
      \item $B\cup F$ ;
      \item $A\cup \bar{F}$ ;
      \item $A\cap \bar{F}$ ;
      \item $A\cap K \cap F$ ;
      \item $A\cup K \cup F$ ;
      \item $\bar{A}\cap \bar{K}$ ;
      \item $\bar{A}\cup \bar{K}$ ;	  
      \end{multicols}
      \end{enumerate}
\end{enumerate}


\sectionblack{Venn diagram}
\begin{enumerate}
\item Let $\Omega$ be an universe, $A$ and $B$ two subsets of $\Omega$. Illustrate with Venn diagrams the following situations :
      \begin{enumerate}
      \item $\Omega=\{1;2;3;4;5;6\} ; A=\{1;5;6\}$ and $B=\{2;5\}$.
      \item $\Omega$=\{blue;white;red;yellow\} ; $A=$\{blue;yellow\} and $B=$\{red\}.
      \item $\Omega=\{a;b;c;d;e;f;g\} ; A=\{a;b;f;g;e\}$ and $B=\{b;c;d\}$.
      \end{enumerate}
\item in a class with 25 students, 15 play music, 8 play chess and 3 play both music and chess.
      \begin{enumerate}
       \item Draw the Venn diagram related to the situation.
       \item How many students play neither music nor chess ?
      \end{enumerate}
\end{enumerate}

\end{document}
