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\item \lect Use the DPLL algorithm with \textit{Boolean Constrain Propagation} and \textit{Pure Literals} (\emph{without} clause learning) to determine whether or not the set of clauses given is satisfiable. Decide variables in alphabetical order starting with the \textit{positive} phase. If the set of clauses resulted in \texttt{SAT}, give a satisfying model.
\begin{dpllCNFInput} \item $(\lnot a \lor b)$ \item $(\lnot b \lor c)$ \item $(\lnot c \lor d)$ \item $(\lnot d \lor e)$ \item $(\lnot e \lor \lnot a)$\end{dpllCNFInput}
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