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

question 18

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.
- $$\neg \exists x \exists y ( P ( x , y ) \wedge \neg P ( y , x ) )$$

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Definitions:

Community

A group of people living in the same place or having a particular characteristic in common.

Argument from Analogy

A form of reasoning in which a similarity between two or more things is used to suggest that what is true of one thing must also be true of the others, especially in cases lacking direct evidence.

Other Minds

The philosophical problem concerning the nature of understanding or knowing the existence of and thoughts or feelings of others.

Self-identity

An individual's perception of themselves, including aspects of their personality, values, beliefs, and roles in various social contexts.