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21 lines
626 B
21 lines
626 B
\item \self Given is the following formula in predicate logic
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$$\phi = \forall x \exists y \Bigl(
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\bigl(
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Q(x,y) \wedge P(x,y)
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\bigr)
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\implies
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\bigl(
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R(y, x) \wedge P(x,y)
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\bigr)
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\Bigr) $$
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and the model $\mathcal{M}$:
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\begin{itemize}
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\item $\mathcal{A} = \{a, b\} $
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\item $P^\mathcal{M} = \{(m,a) | m \in \mathcal{A} \}$
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\item $Q^\mathcal{M} = \{(b,m) | m \in \mathcal{A} \}$
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\item $R^\mathcal{M} = \{(a,b),(b,a), (b,b) \}$
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\end{itemize}
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Does the model $\mathcal{M}$ satisfy the formula $\phi$?
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Explain your answer by drawing a \textbf{syntax tree} and evaluate the model $\mathcal{M}$ with the help of this syntax tree.
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