Using the truth table for the predicate $P$ over the domain $D=\{a,b,c\}$, where the first argument is the row of our truth table and the second is the column. For example, $P(b,c) = F$, whereas $P(c,b) = T$.
Evaluate the truth values of the following predicate logic statement.
$$\exists x \forall y, P(y,x)$$
Edit: Putting your statement into words: "exists a column such that its intersection with all rows is True". No column meets the condition, so the statement is False.