434/assignment 1.tex

   1 \documentclass[11pt,a4paper]{article}
   2
   3 \usepackage{fullpage, amssymb, amsthm, enumerate, amsmath, pictexwd, mathrsfs, ../dcpic, ../yomcat}
   4
   5 \pagestyle{empty}
   6
   7 \setlength{\arraycolsep}{2pt}
   8 \setlength{\parskip}{1ex}
   9 \setlength{\parindent}{0pt}
  10
  11 \begin{document}
  12
  13 \begin{center}
  14 {\bf Victoria University of Wellington}\\[1ex]
  15 {\bf School of Mathematics, Statistics \& Operations Research}\\
  16 \end{center}
  17
  18 \hrule
  19 MATH 434 \hfill
  20 Assignment 1 \hfill
  21 Michael Welsh (301012788)
  22 \vspace{1ex}\hrule\vspace{1ex}
  23
  24 \begin{enumerate}
  25         \item \begin{enumerate}
  26                 \item \tuple{x,y} = \tuple{u,v} iff \set{\set{x},\set{x,y}} = \set{\set{u},\set{u,v}}. \\
  27                 From this, there are four cases (as LHS $\subseteq$ RHS): \begin{enumerate}
  28                         \item \set{x} = \set{u} and \set{x,y} = \set{u}: \\
  29                         So $x = u$ and $y = u$. As RHS $\subseteq$ LHS, $x = u = y = v$.
  30                         \item \set{x} = \set{u} and \set{x,y} = \set{u,v}: \\
  31                         \item \set{x} = \set{u,v} and \set{x,y} = \set{u}: \\
  32                         \item \set{x} = \set{u,v} and \set{x,y} = \set{u,v}: \\
  33                 \end{enumerate}
  34                 \item
  35                 \item
  36                 \item
  37                 \item
  38         \end{enumerate}
  39         \item \begin{enumerate}
  40                 \item
  41                 \item
  42                 \item
  43                 \item
  44                 \item
  45                 \item
  46                 \item
  47                 \item
  48                 \item
  49                 \item
  50                 \item
  51         \end{enumerate}
  52         \item \begin{enumerate}
  53                 \item
  54                 \item
  55                 \item
  56                 \item
  57         \end{enumerate}
  58         \item \begin{enumerate}
  59                 \item
  60                 \item
  61                 \item
  62                 \item
  63                 \item
  64         \end{enumerate}
  65         \item \begin{enumerate}
  66                 \item
  67                 \item
  68                 \item
  69                 \item
  70         \end{enumerate}
  71 \end{enumerate}
  72
  73 \end{document}