Final answer:
The complement of set A and B (A' and B') are the numbers not included in A or B. Since A union B includes 1, 2, 3, their complements would be the rest of the sample space, numbers 4 through 9. Thus, A' intersect B' is the set {4, 5, 6, 7, 8, 9}.
Step-by-step explanation:
The provided sample space is given as 1, 2, 3, 4, 5, 6, 7, 8, 9, and we're told A union B = 1, 2, 3. To find A' intersect B', we first need to understand the complements. The complement of a set in relation to a sample space consists of all the elements in the sample space that are not in the set. Therefore, A' is the set of numbers in the sample space that are not in A, and similarly, B' is the set of numbers in the sample space that are not in B.
Since A union B = 1, 2, 3, this means that all the elements of A and B are within these three numbers. The complements A' and B', therefore, would consist of the numbers 4, 5, 6, 7, 8, 9 since neither A nor B have these elements. The intersection of A' and B' is simply the set containing these numbers since these are the numbers that are neither in A nor in B.
Therefore, A' intersect B' is the set {4, 5, 6, 7, 8, 9}.