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:

Sleeping Clusters

Groups in which animals sleep closely together for warmth, protection, or social bonding.

Predator

An organism that survives by hunting and consuming other organisms for food, often influencing the structure of ecosystems.

Males

The male sex of a species, characterized by traits, reproductive roles, and secondary sexual characteristics that differ from the female sex.

Selfish Herd Hypothesis

A theory suggesting that individuals can reduce their predation risk by positioning themselves within a group, thus exploiting the protection offered by the collective.