Final answer:
The set A, consisting of all odd positive integers, has a complement A' that includes all even positive integers, zero, and negative integers. In this case, A' correctly describes the complement as it contains all even positive integers, which are not part of A.
Step-by-step explanation:
Given that A represents the set of all odd positive integers, the complement of set A, denoted as A', would contain all outcomes in the sample space that are not odd positive integers. By definition, A' consists of all positive integers that are even, zero, and all negative integers since those are not included in A.
Therefore, looking at the choices provided, A' = x ∈ U and is an even positive integer appropriately describes A' because it specifies that the elements of A' should be even and positive (which are not odd and therefore not in set A).
Remember, in probability terms, P(A) is the probability of event A, and P(A') is the probability of event A'. The sum of P(A) and P(A') is always equal to 1 since A' includes all outcomes not in A. For example, if A = {1, 3, 5} then A' would include the remaining outcomes {2, 4, 6}, assuming the sample space is {1, 2, 3, 4, 5, 6}.