From 0bcb3d4371d77cfb6661ff07be53fefdba9e1ceb Mon Sep 17 00:00:00 2001
From: Jim Martens <jim1@live.de>
Date: Wed, 5 Nov 2014 11:11:51 +0100
Subject: [PATCH] FGI2: Aufgabe 4.3 und 4.4 bearbeitet

---
 fgi2/Blatt4/Aufgabenblatt4.tex | 70 ++++++++++++++++++++++++++++++++++
 1 file changed, 70 insertions(+)
 create mode 100644 fgi2/Blatt4/Aufgabenblatt4.tex

diff --git a/fgi2/Blatt4/Aufgabenblatt4.tex b/fgi2/Blatt4/Aufgabenblatt4.tex
new file mode 100644
index 0000000..b30443c
--- /dev/null
+++ b/fgi2/Blatt4/Aufgabenblatt4.tex
@@ -0,0 +1,70 @@
+\documentclass[10pt,a4paper,oneside,ngerman,numbers=noenddot]{scrartcl}
+\usepackage[T1]{fontenc}
+\usepackage[utf8x]{inputenc}
+\usepackage[ngerman]{babel}
+\usepackage{amsmath}
+\usepackage{amsfonts}
+\usepackage{amssymb}
+\usepackage{paralist}
+\usepackage{gauss}
+\usepackage{pgfplots}
+\usepackage[locale=DE,exponent-product=\cdot,detect-all]{siunitx}
+\usepackage{tikz}
+\usetikzlibrary{automata,matrix,fadings,calc,positioning,decorations.pathreplacing,arrows,decorations.markings}
+\usepackage{polynom}
+\usepackage{multirow}
+\usepackage[german]{fancyref}
+\polyset{style=C, div=:,vars=x}
+\pgfplotsset{compat=1.8}
+\pagenumbering{arabic}
+% ensures that paragraphs are separated by empty lines
+\parskip 12pt plus 1pt minus 1pt
+\parindent 0pt
+% define how the sections are rendered
+\def\thesection{4.\arabic{section})}
+\def\thesubsection{\arabic{subsection}.}
+\def\thesubsubsection{(\roman{subsubsection})}
+% some matrix magic
+\makeatletter
+\renewcommand*\env@matrix[1][*\c@MaxMatrixCols c]{%
+  \hskip -\arraycolsep
+  \let\@ifnextchar\new@ifnextchar
+  \array{#1}}
+\makeatother
+
+\begin{document}
+\author{Benjamin Kuffel, Jim Martens\\Gruppe 6}
+\title{Hausaufgaben zum 10. November}
+\maketitle
+
+\setcounter{section}{2}
+\section{} %4.3
+	\subsection{}
+	\begin{alignat*}{2}
+		L(TS_{kuchen\_teil}) &=& (v(htwb^{*}k)^{*}o + r)^{*} \\
+		L^{\omega}(TS_{kuchen\_teil}) &=& (v(htwb^{*}k)^{*}o + r)^{\omega}
+	\end{alignat*}
+	\subsection{}
+	\[
+		SS(M) = 1(3(5763)^{*}1 + 1)^{\omega}
+	\]
+	\subsection{}
+	\[
+		ES(M) = 1(3(5763)^{*}1 + 1)^{\omega}
+	\]
+	\subsection{}
+	\begin{alignat*}{2}
+		Sat(Teig \vee \lnot Hitze) &=& \{1, 4, 5\} \\
+		Sat(\lnot Teig) &=& \{1, 2, 3, 6, 7\}
+	\end{alignat*}	
+	
+\section{} %4.4
+	\begin{tabular}{l|l|l}
+		\(f\) & \(M_{kuchen} \models f \) & \(M_{kuchen}, \pi \models f\)\\
+		\hline
+		\(\lozenge \square(\lnot Teig \vee Hitze) \)& nein & nein \\
+		\(\square	\lozenge(\lnot Teig \vee Hitze)\) & ja & ja \\
+		\(\square	(Hitze \;\mathcal{U}\; Backen)\) & nein & nein \\
+		\(\square	\lozenge (Hitze \Rightarrow XX\lnot Backen)\) & ja & ja
+	\end{tabular}
+\end{document}