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

question 38

True/False

suppose 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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Definitions:

Double Negative

A grammatical construction where two forms of negation are used in the same sentence, often resulting in a positive statement.

Not Snowing

The condition or fact of it not being a time or event during which snow is falling from the sky.

Snowing

The precipitation of snowflakes from the atmosphere, usually resulting in a white covering of the ground.

Proposition

A proclamation that asserts a judgment or opinion.