Question

Suppose that Pis a relation on the set of integers defined by Py if and only if I = y2 Is P transitive? Select one:

a. No, P is not transitive.
b. Yes, P is transitive.
c. We can't tell because it depends on the choice of x and y.

Answer 1

The relation P on the set of integers defined by P(y) if and only if y² = x is not transitive. Hence, a) is correct.

Step-by-step explanation:

The relation P on the set of integers defined by P(y) if and only if y² = x is not transitive. In order for a relation to be transitive, it must satisfy the condition that if (x, y) and (y, z) are both in the relation, then (x, z) must also be in the relation. Let's consider an example:

If we have (2, 4) and (4, 16) in the relation, since 2² = 4 and 4² = 16, both pairs satisfy the relation.

However, if we check the pair (2, 16), we can see that 2² = 4 but 16² = 256.

Therefore, (2, 16) is not in the relation and P is not transitive.