Final answer:
Three sets divide the universal set into at most 7 regions, as visualized by a Venn diagram with individual sets, pair intersections, and a common intersection point.
Step-by-step explanation:
When considering three sets that divide the universal set, they can often be represented using a Venn diagram. Each set can be visualized as a circle within a rectangle representing the universal set. The maximum number of regions these three circles (sets) can divide the universal set into is calculated by considering the individual areas and their possible intersections.
To calculate the maximum regions, we look at the individual sets (3), the two-set intersections (3 choose 2, which is 3), and the one region where all three sets intersect (1). Adding these up gives us 3 + 3 + 1 = 7 regions. Thus, three sets can divide the universal set into at most 7 regions.