P(x, y) is a predicate and the universe for the variables x and y is {1, 2, 3}. Suppose
P(1, 3), P(2, 1), P(2, 2), P(2, 3), P(3, 1), P(3, 2) are true, and P(x, y) is false otherwise. Determine whether
the following statements are true.
-$$\forall x \exists y P ( x , y )$$

Question

Quizplus · Accepted Answer

For each x in the universe {1, 2, 3}, there exists a y such that P(x, y) is true: for x=1, y=3; for x=2, y=1; for x=3, y=1.

P(x, Y) Is a Predicate and the Universe for the Variables