\documentclass{article}
\usepackage{graphicx}
\usepackage{listings}
\usepackage{color}
\usepackage{fancyhdr}
\pagestyle{fancy}
\lhead{Navid Sassan, sassanav, 17-740-812}
\chead{}
\rhead{}
\lfoot{}
\rfoot{}
\cfoot{\thepage}

\usepackage{listings}
\usepackage{color}
\usepackage{tikz}
\usepackage{qtree}
\usepackage{amssymb}

\def\ojoin{\setbox0=\hbox{$\bowtie$}%
  \rule[-.02ex]{.25em}{.4pt}\llap{\rule[\ht0]{.25em}{.4pt}}}
\def\leftouterjoin{\mathbin{\ojoin\mkern-5.8mu\bowtie}}
\def\rightouterjoin{\mathbin{\bowtie\mkern-5.8mu\ojoin}}
\def\fullouterjoin{\mathbin{\ojoin\mkern-5.8mu\bowtie\mkern-5.8mu\ojoin}}

\usetikzlibrary{automata, positioning, arrows}
\tikzset{
    ->, % makes the edges directed
    >=stealth', % makes the arrow heads bold
    node distance=3cm, % specifies the minimum distance between two nodes. Change if necessary.
    every state/.style={thick, fill=gray!10}, % sets the properties for each ’state’ node
    initial text=$ $, % sets the text that appears on the start arrow
}

\definecolor{mygreen}{rgb}{0,0.6,0}
\definecolor{mygray}{rgb}{0.5,0.5,0.5}
\definecolor{mymauve}{rgb}{0.58,0,0.82}

\lstset{ %
	backgroundcolor=\color{white},   % choose the background color; you must add \usepackage{color} or \usepackage{xcolor}; should come as last argument
	basicstyle=\footnotesize,        % the size of the fonts that are used for the code
	breakatwhitespace=false,         % sets if automatic breaks should only happen at whitespace
	breaklines=true,                 % sets automatic line breaking
	captionpos=b,                    % sets the caption-position to bottom
	commentstyle=\color{mygreen},    % comment style
	deletekeywords={...},            % if you want to delete keywords from the given language
	escapeinside={\%*}{*)},          % if you want to add LaTeX within your code
	extendedchars=true,              % lets you use non-ASCII characters; for 8-bits encodings only, does not work with UTF-8
	frame=single,	                   % adds a frame around the code
	keepspaces=true,                 % keeps spaces in text, useful for keeping indentation of code (possibly needs columns=flexible)
	keywordstyle=\color{blue},       % keyword style
	language=Octave,                 % the language of the code
	morekeywords={*,...},            % if you want to add more keywords to the set
	numbers=left,                    % where to put the line-numbers; possible values are (none, left, right)
	numbersep=5pt,                   % how far the line-numbers are from the code
	numberstyle=\tiny\color{mygray}, % the style that is used for the line-numbers
	rulecolor=\color{black},         % if not set, the frame-color may be changed on line-breaks within not-black text (e.g. comments (green here))
	showspaces=false,                % show spaces everywhere adding particular underscores; it overrides 'showstringspaces'
	showstringspaces=false,          % underline spaces within strings only
	showtabs=false,                  % show tabs within strings adding particular underscores
	stepnumber=1,                    % the step between two line-numbers. If it's 1, each line will be numbered
	stringstyle=\color{mymauve},     % string literal style
	tabsize=2,	                   % sets default tabsize to 2 spaces
	title=\lstname                   % show the filename of files included with \lstinputlisting; also try caption instead of title
}

\begin{document}

\section{Aufgabe 1}

\subsection{1}
\begin{tabular}{ |c|c| }
    \hline
    B & C \\
    \hline
    0 & 1 \\
    \hline
\end{tabular}

\subsection{2}
\begin{tabular}{ |c|c|c| }
    \hline
    D & B & C \\
    \hline
    1 & 0 & 1 \\
    0 & 0 & 1 \\
    \hline
\end{tabular}


\section{Aufgabe 2}

\subsection{1}
$\Pi_{Kaffehaeuser}(\sigma_{s.Kuchen \neq v.Kuchen}((g \bowtie s) \bowtie v))$

\subsection{2}
$\Pi_{Besucher}(\sigma_{Kuchen = NULL}(\sigma_{(Kaffehaus = 'Spruengli' or Kaffehaus = 'Cafe Sacher')}(g)\leftouterjoin v)$


\section{Aufgabe 3}

\subsection{1}
\begin{tabular}{ |c|c| }
    \hline
    C & D \\
    \hline
    3 & 0 \\
    \hline
    4 & 0 \\
    \hline
\end{tabular}

\subsection{2}
\begin{tabular}{ |c|c|c|c| }
    \hline
    D & B & C & A \\
    \hline
    0 & 1 & 3 & 0 \\
    \hline
    0 & 1 & 3 & 7 \\
    \hline
\end{tabular}



\end{document}
