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\title{CSCI 301 - Assignment 1, Fall 2024}
\author{Your name here}
\date{}

\newcommand{\answer}{%
  \par\noindent%
  \textbf{Answer\\}%
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\begin{document}

\maketitle

\noindent
Modify the .tex source file for this document, replacing the placeholders with
your solutions. \\
This is an individual assignment. See the syllabus for the collaboration policy.\\

\hrule

% Beginning of Questions
\begin{enumerate}
\item (3 points) Write the following set using set builder notation: 
$\{...,-4,-1, 2, 5, 8, 11, 14, 17,...\}$

\answer
\emph{Replace this text, including the emphasis, with your answer.}

\item (3 points) Write the set of all rational numbers using set builder notation and
without using $\mathbb{Q}$.

\answer
\emph{Replace this text, including the emphasis, with your answer.}

\item (3 points) Explicitly write out the contents of the following set: 
$\{X\in \mathcal{P}(\{1,2,3\}) : 2 \in X\}$

\answer
\emph{Replace this text, including the emphasis, with your answer.}


\item (6 points) Let $S = \{\mathbb{Z}, 1, \{1, 2\}, \{\varnothing\}\}$. Indicate whether
each of the following statements is True or False.
\begin{enumerate} 
\item $|S| = 4$  \inlineanswer \emph{Replace this text, including emphasis, with True or False}
\item $1 \in S$  \inlineanswer \emph{Replace this text, including emphasis, with True or False}
\item $2 \in S$  \inlineanswer \emph{Replace this text, including emphasis, with True or False}
\item $\varnothing \in S$  \inlineanswer 
      \emph{Replace this text, including emphasis, with True or False}
\item $\varnothing \subseteq S$  
      \inlineanswer \emph{Replace this text, including emphasis, with True or False}
\item $\mathbb{Z} \subseteq S$  
      \inlineanswer \emph{Replace this text, including emphasis, with True or False}
\end{enumerate}

\item (5 points) Suppose we define the following sets:
\begin{itemize}
    \item $A = \{1, 2\}$
    \item $B = \{\varnothing\}$
    \item $C = \varnothing$
    \item $D = \{\varnothing, \{1,3\}\}$
\end{itemize} 
Compute each of the following Cartesian products. Add your answer to the existing line:
\begin{enumerate}
        \item $A \times B = $

        \item $A \times C = $

        \item $A \times D = $
\end{enumerate}
\end{enumerate}

\end{document}

