Questionnaire-2024/propositional_logic/1018_sol.tex

Let $\Model_1 = \{p=\F, q=\F, r=\F\}$ and $\Model_2 = \{p=\F, q=\F, r=\T\}$ and annotate the parse tree with in blue for $\Model_1$ and red for $\Model_2$.

\begin{center}
\begin{forest}
for tree={circle, draw,
          minimum size=2em,
          inner sep=0pt,
          s sep=6mm,
          l sep=7mm}
  [$\land$, label={\satUnsatAss{T}{F}}
    [$\imp$, label={\satUnsatAss{T}{F}}
      [$\neg$, edge label={node[midway,left]{\satUnsatAss{F}{T}}}
        [$\biimp$, label={\satUnsatAss{T}{F}}
          [$r$, label={\satUnsatAss{F}{T}}]
          [$q$, label={\satUnsatAss{F}{F}}]
        ]
      ]
      [$\neg$,label={\satUnsatAss{T}{F}}
        [$r$, label={\satUnsatAss{F}{T}}]
      ]
    ]
    [$\lor$, label={\satUnsatAss{T}{T}}
      [$\neg$, label={\satUnsatAss{F}{T}}
        [$\imp$, label={\satUnsatAss{T}{F}}
          [$r$, label={\satUnsatAss{F}{T}}]
          [$q$, label={\satUnsatAss{F}{F}}]
        ]
      ]
      [$\imp$, label={\satUnsatAss{T}{T}}
        [$p$, label={\satUnsatAss{F}{F}}]
        [$q$, label={\satUnsatAss{F}{F}}]
      ]
    ]
  ]
\end{forest}
\end{center}