Final answer:
At least one of the two integers x or y must be 5 or greater to achieve a product xy ≥ 9 since integer products where both factors are less than 5 are inadequate to reach or exceed the value 9.
Step-by-step explanation:
To prove that if xy ≥ 9, then either x ≥ 5 or y ≥ 5, let's consider the possible products of two integers that are greater than or equal to 9. The pairs of integers that multiply to give a product of 9 or larger, where both integers are less than 5, are limited. For example, 3×4=12 and 4×4=16. But if we have a pair where both numbers are less than 5, like 4×4, it is impossible to obtain a product that is 9 or more. Consequently, at least one of the integers must be 5 or greater to achieve a product of 9 or greater. Therefore, if xy ≥ 9 is true, then either x must be at least 5 or y must be at least 5 or both.