Identify the diagram that best represents the relationship among the classes…

CONCEPT: In a Venn diagram, overlapping circles show that sets can share members. When no class is a strict subset of another and membership can overlap in different ways, the suitable diagram uses separate circles that intersect.

The common overlapping part represents members that may belong to all the relevant classes at the same time.

APPLICATION: Boys, students, and athletes are independent classes. Some boys can be students, some students can be athletes, some boys can be athletes, and a boy can also be both a student and an athlete.

So the relationship needs three circles that all overlap each other, including a central common region.

• Three circles in a chain: it leaves the two end circles without a direct overlap, so it treats one possible pair as unrelated.

• One large circle with two separate small circles: it makes two classes strict subsets of a third and keeps those two classes apart.

• One nested pair with a separate circle: it makes one class wholly inside another and treats the third class as unrelated.

Result: the diagram with three mutually overlapping circles best represents Boys, Students, and Athletes.