Questionnaire-2024/sat_solvers_dpll/0002_sol.tex

\textbf{Definition - Unit Clause.} A clause $c$ is said to be a unit clause
under some assignment $A$ if the following two conditions hold:
\begin{enumerate}
    \item The clause $c$ is not satisfied by $A$.
    \item All but one of the variables in $c$ are given a value by $A$.
\end{enumerate}
Therefore, there is a single literal left in the set representing the clause under the assignment.

An example would be:
\begin{itemize}
  \item $c = \{a, b, \lnot c\}$
  \item $A = \{\lnot a, c\}$
  \item $c[A] = \bot \lor b \lor \bot$, in set representation: $\{b\}$
\end{itemize}