% Sample Question document for STA256
\documentclass[12pt]{article} 
%\usepackage{amsbsy} % for \boldsymbol and \pmb 
%\usepackage{graphicx} % To include pdf files!
\usepackage{amsmath}
\usepackage{amsbsy}
\usepackage{amsfonts}
\usepackage[colorlinks=true, pdfstartview=FitV, linkcolor=blue, citecolor=blue, urlcolor=blue]{hyperref} % For links
\usepackage{fullpage}
%\pagestyle{empty} % No page numbers


\begin{document}
%\enlargethispage*{1000 pt} 

\begin{center}   
{\Large \textbf{Sample Questions: Sets}}%\footnote{}
\vspace{1 mm}

STA256 Fall 2019. Copyright information is at the end of the last page.
\end{center}

\vspace{5mm}
\begin{enumerate} 

\item Draw a Venn diagram illustrating a distributive law:
    \begin{enumerate}
        \item $A \cap (B \cup C)$. \vspace{40mm}
        \item $(A \cap B) \cup (A \cap C)$  \vspace{40mm}
    \end{enumerate}

\item Draw a Venn diagram  illustrating a distributive law: 
    \begin{enumerate}
        \item $A \cup (B \cap C)$. \vspace{40mm}
        \item $(A \cup B) \cap (A \cup C)$  \vspace{40mm}
    \end{enumerate}

\pagebreak


\item Draw a Venn diagram illustrating a De Morgan law:
    \begin{enumerate}
        \item $(A \cap B)^c$. \vspace{40mm}
        \item $A^c \cup B^c$  \vspace{40mm}
    \end{enumerate}

\item Draw a Venn diagram illustrating a De Morgan law: 
    \begin{enumerate}
        \item $(A \cup B)^c$. \vspace{40mm}
        \item $A^c \cap B^c$  \vspace{40mm}
    \end{enumerate}

\pagebreak

\item Draw a Venn diagram showing that if $A$ and $B$ are disjoint, then $A \cap C$ and $B \cap C$ are also disjoint.


\end{enumerate}

\vspace{150mm}

\noindent
\begin{center}\begin{tabular}{l}
\hspace{6in} \\ \hline
\end{tabular}\end{center}
This assignment was prepared by  \href{http://www.utstat.toronto.edu/~brunner}{Jerry Brunner},
Department of Mathematical and Computational Sciences, University of Toronto. It is licensed under a 
\href{http://creativecommons.org/licenses/by-sa/3.0/deed.en_US}
     {Creative Commons Attribution - ShareAlike 3.0 Unported License}. Use any part of it as you like and share the result freely. The \LaTeX~source code is available from the course website: 
     
\begin{center}
\href{http://www.utstat.toronto.edu/~brunner/oldclass/256f19} {\small\texttt{http://www.utstat.toronto.edu/$^\sim$brunner/oldclass/256f19}}
\end{center}

\end{document}