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\usepackage[margin=1in]{geometry}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage[T1]{fontenc} % Fix ASCII symbols in text mode
\usepackage[utf8]{inputenc} % Allow unicode characters
\usepackage{enumitem} % Alphabetic enumeration
\usepackage{graphicx} % Embedding images

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% Symbol shortcuts
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\textbf{Question #1:}}
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\begin{document}

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\setlength{\parindent}{0em}

\section*{Written Assignment 5}

\begin{question}{1}
Define the following terms and provide an example of each:
\begin{itemize}
\item A set
\item Set union
\item Set intersection
\item Set difference
\item Set complement
\item $\mathcal{P}(X)$ of set $X$
\item Cartesian/cross product
\end{itemize}
\end{question}

\begin{question}{2}
Write the following using mathematical notation:
\begin{itemize}
\item Associativity of union
\item Associativity of intersection
\item Commutativity of union
\item Commutativity of intersection
\item Distributive law for union
\item Distributive law for intersection
\end{itemize}
\end{question}

\begin{question}{3}
Solve book problem 5.1.
\end{question}

\begin{question}{4}
Are each of the following statements true or false? If true, explain why. If false, provide a counterexample.\\
\textbf{Note:} A convincing explanation is sufficient for the true statements (formal proofs are not required).
\begin{itemize}
\item $X \times Y \times Z  = Z \times Y \times X$
\item $B - A = A - B$
\item $A \times (B \cup C) = (A \times B) \cup (A \times C)$
\item $B \times B = B$  
\item $A - (B \cap C) = (A - B) \cup (A - C)$
\end{itemize}
\end{question}

\begin{question}{5}
Describe the following sets using set-builder notation:
\begin{itemize}
\item The set of all positive real numbers
\item The set of all integers divisible by 2 or 3
\item The set of irrational numbers
\end{itemize}
\end{question}

\begin{question}{6}
Consider three sets: B, F, and V.
Set B represents students who play basketball,
set F represents students who play football, and
set V represents students who play volleyball.\\\\
%
\textbf{Draw a Venn diagram} illustrating the following information:\\
30 students play basketball.\\
25 students play football.\\
20 students play volleyball.\\
10 students play both basketball and football.\\
5 students play both basketball and volleyball.\\
8 students play both football and volleyball.\\
3 students play all three sports.\\\\
%
Use your Venn diagram to calculate how many students:
\begin{itemize}
\item Play \textbf{only} basketball
\item Play only one sport
\item Play only two sports
\item Play \textbf{at least one} sport
\item Play \textbf{at least two} sports
\end{itemize}

Embed a scan of your Venn diagram below (see commented instructions).
\end{question}

% Replace "yourimage" with the file name of an image of your Venn diagram, then uncomment this code to embed your image.
%\begin{figure}[h]
%\centering
%\includegraphics[width=.8\linewidth]{yourimage}
%\end{figure}

\end{document}
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