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% Assignment 0b for CS3530 Computational Theory:
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% Fall 2024
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\textbf{\Large CS 3530: Assignment 0b} \\[2mm]
Fall 2024

\emph{Your Name Here}
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\section*{Exercise 0.1def (6 points)}

\subsection*{Problem}

Examine the following formal descriptions of sets so that you understand which members they contain.  Write a short informal English description of each set.

\begin{itemize}
\item[d.] $\{ n | n = 2m $ for some $m$ in $\mathbb{N}$, and $n = 3k$ for some $k$ in $\mathbb{N} \}$

\textbf{Solution}

\emph{Your Solution Here}

\item[e.] $\{ w | w $ is a string of $0$s and $1$s and $w$ equals the reverse of $w \}$

\textbf{Solution}

\emph{Your Solution Here}

\item[f.] $\{ n | n $ is an integer and $n = n + 1 \}$

\textbf{Solution}

\emph{Your Solution Here}

\end{itemize}

\section*{Exercise 0.2b (2 points)}

\subsection*{Problem}

Write formal descriptions of the following sets.

\begin{itemize}
\item[b.] The set containing all integers that are greater than 5.

\textbf{Solution}

\emph{Your Solution Here}

\end{itemize}

\section*{Exercise 0.3abcdef (12 points)}

\subsection*{Problem}

Let $A$ be the set $\{ x, y, z \}$ and $B$ be the set $\{ x, y \}$.

\begin{itemize}
\item[a.] Is $A$ a subset of $B$?

\textbf{Solution}

\emph{Your Solution Here}

\item[b.] Is $B$ a subset of $A$?

\textbf{Solution}

\emph{Your Solution Here}

\item[c.] What is $A \cup B$?

\textbf{Solution}

\emph{Your Solution Here}

\item[d.] What is $A \cap B$?

\textbf{Solution}

\emph{Your Solution Here}

\item[e.] What is $A \times B$?

\textbf{Solution}

\emph{Your Solution Here}

\item[f.] What is the power set of $B$?

\textbf{Solution}

\emph{Your Solution Here}

\end{itemize}

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