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\title{Recitation 9}
\author{Created by Taylor Spangler, Adapted by Beau Christ}
\date{\today}

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\maketitle

\begin{itemize}
\ig{\item (3 min max) Questions about last week's quiz?
\item Questions about lecture / homework so far?
}
\item Given the Poset: $(\{\{1\},\{2\},\{4\},\{1,2\},\{1,4\},\{2,4\},\{3,4\},\{1,3,4\},\{2,3,4\}\},\subseteq)$
\begin{enumerate}
\item Find the maximal elements:$\{1,2\}, \{1,3,4\},\{2,3,4\}$ (because these are not subsets of any other sets in the relation right?)
\item Find the minimal elements$: \{1\},\{2\},\{4\}$ (again, there are no subsets of these sets in the relation)
\item Is there a maximum (i.e., greatest) element?: No.  It does not exist.
\item Is there a minimum (i.e., least) element?: No.  It does not exist.
\item Find the set of all upper bounds of $\{\{2\},\{4\}\}$: $\{\{2,4\},\{2,3,4\}\}$
\item Find the least upper bound (lub) of $\{\{2\},\{4\}\}$: the element $\{2,4\}$
\item Find the set of all lower bounds of $\{\{1,3,4\},\{2,3,4\}$: $\{\{3,4\},\{4\}\}$
\item Find the greatest lower bound (glb) of $\{\{1,3,4\},\{2,3,4\}\}$: the element \{3,4\}
\end{enumerate}


\end{itemize}

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