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

question 86

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

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Definitions:

Probability

The measure of the likelihood that an event will occur, quantified as a number between 0 and 1, where 0 means the event will not happen, and 1 means it will definitely happen.

Jelly Beans

Small, bean-shaped sugar candies with soft candy shells and thick gel interiors, available in various flavors.

Proportion

A statistical measure that reflects the fraction of the total number of items in a particular category.

Standard Deviations

A measure that quantifies the amount of dispersion or variability of a set of data points or distribution from its mean.