%
% LaTeX Problem Set Template originally designed
% by former CS103 TA Sachin Padmanabhan, with updates,
% edits, and simplifications by the lovely folks below.
%
% Updated for Fall 2018 by Michael Zhu
% Updated for Fall 2019 by Joshua Spayd
% Updated for Fall 2020 by Lucy Lu
% Updated for Winter/Spring 2021 by Cynthia Bailey Lee
% Updated for Fall 2021 by Grant McClearn
% Commands slimmed down and simplified in Fall 2022 by Keith Schwarz

\documentclass{article}
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\title{CS 103: Mathematical Foundations of Computing\\Problem Set \#4}
\author{[TODO: Replace this with your name(s)]}
\date{\today}

% Running author based on https://tex.stackexchange.com/questions/68308/how-to-add-running-title-and-author#answer-68310
\makeatletter
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\lhead{\runauthor}
\chead{Problem Set 4}
\rhead{\today}
\lfoot{}
\cfoot{CS 103: Mathematical Foundations of Computing --- Fall 2022}
\rfoot{\thepage}

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\begin{document}

\maketitle

\maketitle

\begin{center}
  \emph{Due Friday, October 28 at 2:30 pm Pacific}
\end{center}

\vspace{1cm}

Sets can be written as $\Set{1, 2, 3}$ or as $\Set{ n \in \naturals \suchthat n \ge 137 }$. \\

Multicharacter superscripts and subscripts need braces: $x^{137x + 42}$ or $x_{137}$.

\newpage

\section*{Problem One: Independent and Dominating Sets}
    i.
    \begin{shaded}
    Write your answer to Problem One, part i. here.
    \end{shaded}
    
    ii.
    \begin{shaded}
    Write your answer to Problem One, part ii. here.
    \end{shaded}
    
    iii.
    \begin{shaded}
    Write your answer to Problem One, part iii. here.
    \end{shaded}
    
    iv.
    \begin{shaded}
    Write your answer to Problem One, part iv. here.
    \end{shaded}

\newpage


\section*{Problem Two: Friends, Strangers, Enemies, and Hats}
    i.
    \begin{shaded}
    Write your answer to Problem Two, part i. here.
    \end{shaded}
    
    ii.
    \begin{shaded}
    Write your answer to Problem Two, part ii. here.
    \end{shaded}

\newpage


\section*{Problem Three: Iterated Injections}
    i.
    \begin{shaded}
    Write your answer to Problem Three, part i. here.
    \end{shaded}
    
    ii.
    \begin{shaded}
    Write your answer to Problem Three, part ii. here.
    \end{shaded}
    
    iii.
    \begin{shaded}
    Write your answer to Problem Three, part iii. here.
    \end{shaded}
    
\newpage

\section*{Optional Fun Problem: Forced Triangles}
\begin{shaded}
Write your answer to the Optional Fun Problem here.
\end{shaded}
    
\end{document}