6.5.3 Predicate calculus

Problem: Determine the truth values of formulas in a given interpretation: a) \( \exists x \forall y(P(x) \Rightarrow Q(y)) \), b) \( \exists x(P(x) \& Q(x)) \) \[ D=\{a, b\} \] \begin{tabular}{|c|c|c|} \hline\( x \) & \( P(x) \) & \( Q(x) \) \\ \hline\( a \) & 1 & 0 \\ \hline\( b \) & 0 & 1 \\ \hline \end{tabular}