To determine the complement of the set A, denoted as Ac, we need to understand what the set A consists of and then identify the elements that are not in this set.
The set A is defined as follows: \[ A = { x | x \in U \text{ and } x \text{ is an odd positive integer} } \] This means A contains all positive odd integers, such as 1, 3, 5, 7, and so on.
The universal set U consists of all positive integers: \[ U = { 1, 2, 3, 4, 5, \ldots } \]
The complement of set A, Ac, will include all positive integers that are not in A. Since A contains all odd positive integers, Ac will include all positive integers that are not odd, which are the even positive integers.
Therefore, the correct description of Ac is: \[ Ac = { x | x \in U \text{ and is an even positive integer} } \]
Hence, the correct answer is: Ac = {x|x ∈ U and is an even positive integer}.