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

Question

Quizplus · Accepted Answer

Explanation:The given statement is true because for every y in the universe {1, 2, 3}, there exists an x such that P(x, y) implies P(y, x). For example, when y = 1, we have P(2, 1) and P(1, 2), which satisfy the implication. Similarly, when y = 2, we have P(2, 2) and P(2, 2), and when y = 3, we have P(3, 1) and P(1, 3). Therefore, the statement is true.

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