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\title{CS 103: Mathematical Foundations of Computing\\Problem Set \#2}
\author{[TODO: Replace this with your name(s)]}
\date{\today}

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\chead{Problem Set 2}
\rhead{\today}
\lfoot{}
\cfoot{CS 103: Mathematical Foundations of Computing --- Winter 2023}
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\begin{document}

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\begin{center}
  \emph{Due Friday, October 14 at 2:30 pm Pacific}
\end{center}

\vspace{1cm}

Problems One through Six are to be answered by editing the appropriate files (see the Problem Set \#2 instructions). You won't include your answers to those problems here.

\section*{Symbols Reference}
Here are some symbols that may be useful for this problem set.

\begin{itemize}
    \item Logical AND: $\land$
    \item Logical OR: $\lor$
    \item Logical NOT: $\lnot$
    \item Logical implies: $\to$
    \item Logical biconditional: $\leftrightarrow$
    \item Logical TRUE: $\top$
    \item Logical FALSE: $\bot$
    \item Universal quantifier: $\forall$
    \item Existential quantifier: $\exists$
\end{itemize}

\LaTeX typing tips:
\begin{itemize}
    \item Sets: $\Set{1, 2, 3}$, $\Set{n \in \naturals \suchthat n \text{ is even}}$
    \item Exponents (use curly braces if exponent is more than 1 character): $x^2$, $2^{3x}$
    \item Subscripts (use curly braces if subscript is more than 1 character): $x_0$, $x_{10}$
\end{itemize}

\newpage

\section*{Problem Seven: Yablo's Paradox}
    i.
    \begin{shaded}
    Write your answer to Problem Seven, part i. here.
    \end{shaded}
    
    ii.
    \begin{shaded}
    Write your answer to Problem Seven, part ii. here.
    \end{shaded}
    
    iii.
    \begin{shaded}
    Write your answer to Problem Seven, part iii. here.
    \end{shaded}
    
\newpage

\section*{Problem Eight: Tournament Champions}
    i.
    \begin{shaded}
    Write your answer to Problem Eight, part i. here.
    \end{shaded}
    
    ii.
    \begin{shaded}
    Write your answer to Problem Eight, part ii. here.
    \end{shaded}

\section*{Problem Nine: Set Theory Proofs

\emph{Theorem:} For all sets $A$ and $B$, if $A \subseteq B$, then $\wp(A \cup B) \subseteq \wp(B)$.

\emph{Proof: } 
    \begin{shaded}
    Write your answer to Problem Nine here.
    \end{shaded}

    
\newpage

\section*{Optional Fun Problem: Insufficient Connectives}

\begin{shaded}
Write your answer to the Optional Fun Problem here.
\end{shaded}
    
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