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\begin{frame}{Proving and Disproving Semantical Entailment}
  \begin{exampleblock}{}
    Which of the following semantic implications are true?
    \begin{talign}
      \text{\hint{(a)}}\quad\quad \formula{\forallst{x}{\existsst{y}{\,\binpred{R}{x}{y}}}} \;\;&\models\;\; \formula{\existsst{x}{\forallst{y}{\,\binpred{R}{x}{y}}}} \quad\quad \alert{NO} \\
      \text{\hint{(b)}}\quad\quad \formula{\forallst{x}{\existsst{y}{\,\binpred{R}{x}{y}}}} \;\;&\models\;\; \formula{\existsst{y}{\forallst{x}{\,\binpred{R}{x}{y}}}} \quad\quad \alert{NO} \\
      \text{\hint{(c)}}\quad\quad \formula{\existsst{y}{\forallst{x}{\,\binpred{R}{x}{y}}}} \;\;&\models\;\; \formula{\forallst{x}{\existsst{y}{\,\binpred{R}{x}{y}}}} \quad\quad \alert{YES} \\
      \text{\hint{(d)}}\quad\quad \formula{\existsst{y}{\forallst{x}{\,\binpred{R}{x}{y}}}} \;\;&\models\;\; \formula{\forallst{y}{\existsst{x}{\,\binpred{R}{x}{y}}}} \quad\quad \alert{NO} 
    \end{talign}
  \end{exampleblock}
\end{frame}