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\usepackage[parfill]{parskip}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{patterns}

\begin{document}

\begin{center}
\Large{CS 191\\}
\large{Homework 2\\}
\end{center}
\begin{flushright}
abc1234
Alan Garvey\\
\today\\
\end{flushright}

\textbf{Problem 1.}  Show the power set of the set $\{x,y,z\}$.\\
\textit{Answer:} The power set is:

%The following defines a Venn diagram containing three overlapping sets and
% labels each distinct part of the overlapping sets.
Here is a labelled Venn Diagram.

\begin{tikzpicture}[thick,fill opacity=0.5]
\draw (0,0) rectangle (10,10);
\draw (4,6) circle (2cm)   (6,6) circle (2cm)  (5,4) circle (2cm);
\draw(2,9) node {$P$};
\draw(3.5,6.5) node {$A$};
\draw(6.5,6.5) node {$B$};
\draw(5,3) node {$C$};
\draw(5,6.5) node {$Q$};
\draw(5,5) node {$S$};
\draw(3.75,5) node {$R$};
\draw(6.25,5) node {$T$};
\end{tikzpicture}

Here is the Venn Diagram for $A \cup B$.

\begin{tikzpicture}[thick,fill opacity=0.5]
\draw (0,0) rectangle (10,10);
\draw (4,6) circle (2cm)   (6,6) circle (2cm)  (5,4) circle (2cm);
% \draw(2,9) node {$P$};
\draw(3.5,6.5) node {$x$};
\draw(6.5,6.5) node {$x$};
% \draw(5,3) node {$C$};
\draw(5,6.5) node {$x$};
\draw(5,5) node {$x$};
\draw(3.75,5) node {$x$};
\draw(6.25,5) node {$x$};
\end{tikzpicture}

\end{document}
