Questionnaire-2024/predicate_logic/0011_sol.tex

\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
\Tree
[.$\imp$ 
    [.$\forall x$ 
        [.$\exists z$
            [.$\lor$
                [.$\lnot$
                    [.$P$ $x$ ]
                    ]
                [.$Q$
                    [.$y$ ]
                    [.$f$ $z$ ]
                ]
            ]
        ]
    ]
    [.$\land$ 
        [.$\exists x$
            [.$\land$
                [.$P$ $y$ ]
                [.$Q$
                    [.$f$ $x$ ]
                    [.$z$ ]
                ]
            ]
        ]
    ]
]
\end{tikzpicture} 
\newline \\
Free variables: $y, z$ \\
Bound variables: $x, z$