# HG changeset patch
# User Eugen Sawin <sawine@me73.com>
# Date 1311013045 -7200
# Node ID becb48258245290aae6e63f83339fbd4f731f15b
# Parent  847768226d252ad06a9daa1bf0e20d10ba30b5e6
First part of ex 9.

diff -r 847768226d25 -r becb48258245 tex/theory1_ex9.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/tex/theory1_ex9.tex	Mon Jul 18 20:17:25 2011 +0200
@@ -0,0 +1,46 @@
+\documentclass[a4paper, 10pt, pagesize, smallheadings]{article}  
+\usepackage{graphicx}
+%\usepackage[latin1]{inputenc}
+\usepackage{amsmath, amsthm, amssymb}
+\usepackage{typearea}
+\usepackage{algorithm}
+\usepackage{algorithmic}
+\usepackage{fullpage}
+\usepackage{mathtools}
+\usepackage[all]{xy}
+\title{Theory I, Sheet 9 Solution}
+\author{Eugen Sawin}
+\renewcommand{\familydefault}{\sfdefault}
+\newcommand{\Pos}{\mathcal{P}os}
+\newcommand{\E}{\mathcal{E}}
+\newcommand{\D}{\mathcal{D}}
+\newcommand{\J}{\mathcal{J}}
+\include{pythonlisting}
+
+\pagestyle{empty}
+\begin{document}
+\maketitle
+
+\section*{Exercise 9.1.3}
+\begin{align*}
+ADT_{bool} = &(\Sigma_{bool}, \E)\\
+\Sigma_{bool} = &\{true^{(0)}, false^{(0)}, not^{(1)}, and^{(2)}, or^{(2)}\}\\
+\E = &\{true \approx not(false),\\
+& false \approx not(true),\\
+& not(not(x)) \approx x\\
+& and(x, y) \approx not(or(not(x), not(y))),\\
+& or(x, y) \approx not(and(not(x), not(y)))\}\\
+\end{align*}
+
+\section*{Exercise 9.1.4}
+\begin{align*}
+\D_{bool} &= (M, \J)\\
+M &= \{0, 1\}\\
+\J(true) &= 1\\
+\J(false) &= 0\\
+\J(not)(x) &= 1 - x\\
+\J(and)(x, y) &= min(x, y)\\
+\J(or)(x, y) &= max(x, y)\\
+\end{align*}
+
+\end{document}