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

question 25

True/False

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.
- $$\forall y \exists x ( P ( x , y ) \rightarrow P ( y , x ) )$$

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