\emph{Satisfying Model:} truth assignment such that the formula resolves to \emph{true}.\\
\emph{Falsifying Model:} truth assignment such that the formula resolves to \emph{false}.\\
We write: $\mathcal{M} \models \varphi$: The model satisfies the formula.\\
and $\mathcal{M} \nmodels \varphi$:  The model does not satisfy the formula.