Final answer:
The predicates that make the statement ∀x p(x) true for all positive integers are those properties that are inherent and universally applicable to every positive integer, such as 'x is greater than 0'.
Step-by-step explanation:
The statement ∀x p(x) states that predicate p is true for every positive integer x. For this to hold true in the domain of positive integers, the predicate p must express a property that is inherent to all positive integers. For example, a predicate that could satisfy this condition would be 'p(x) is greater than 0', since all positive integers are, by definition, greater than 0. In contrast, a predicate such as 'p(x) is an even number' would not satisfy the statement ∀x p(x) because not all positive integers are even. Therefore, the predicates for which ∀x p(x) is true are those that define properties universally applicable to all positive integers.