\item Use the DPLL algorithm with \textit{Boolean Constrain Propagation} (\emph{without} PL and 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 $(\lnot a \lor \lnot b)$
    \item $(\lnot a \lor c)$
    \item $(\lnot b \lor \lnot c)$
    \item $(b \lor c)$
    \item $(a \lor \lnot b)$
\end{dpllCNFInput}