6.5.16 Predicate calculus

Condition: The predicate \( P(x, y) \) is specified in a table, i.e. a table of values ​​of this predicate is given for each pair \( (x, y) \) of values ​​of independent variables \( x, y \). \begin{tabular}{|c|c|c|c|c|c|c|} \hline\( x / y \) & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline 1 & 1 & 0 & 0 & 1 & 1 & 0 \\ 2 & 0 & 1 & 0 & 1 & 1 & 0 \\ 3 & 1 & 1 & 0 & 1 & 1 & 1 \\ 4 & 0 & 1 & 0 & 0 & 0 & 0 \\ \hline \end{tabular} Check the truth of the following statement: \( \exists y \forall x P(x, y) \).