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34 lines
771 B
34 lines
771 B
\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
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\Tree
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[.$\imp$
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[.$\forall x$
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[.$\exists y$
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[.$\land$
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[.$P$
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[.$f$ $y$ ]
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]
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[.$P$ $x$ ]
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]
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]
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]
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[.$Q$
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[.$f$
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[.$f$ $y$ ]
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]
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]
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]
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\end{tikzpicture}
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\newline \\
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Free variables: $y$ \\
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$\mathcal{M}_1: \mathcal{A} = \{a, b\}$ \\
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$P^{\mathcal{M}_1}$ = true \\
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$Q^{\mathcal{M}_1}$ = true \\
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$\mathcal{M}_1 \models \phi$ \\
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$f$ can be defined arbitrarily in this case.
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$\mathcal{M}_2: \mathcal{A} = \{a, b\}$ \\
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$P^{\mathcal{M}_2}$ = true \\
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$Q^{\mathcal{M}_2}$ = false \\
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$\mathcal{M}_2 \not\models \phi$
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$f$ can be defined arbitrarily in this case.
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