# How to evaluate truth value of quantified formula?

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.

$$\exists x \forall y, P(y,x)$$

• What exactly is the difficulty with this? Try to express the statement in English. – Graham Kemp Mar 4 at 2:02