Which of the following diagrams indicates the best relation between…

In a classification-based Venn diagram question, three circles can relate to one another in only a few basic ways: concentric (nested) circles show a strict subset relationship, where every member of the inner group is also a member of the outer group; completely separate circles show two groups with no members in common; and overlapping circles show two groups that share some members without either being a subset of the other. The correct diagram for any set of categories must match how those categories actually relate to one another in real life.

Professors, Doctors and Men are three independent categories, and none of them is a subset of, or completely separate from, any other. A person can be a professor without being a doctor, and a doctor without being a professor, yet some individuals are both (for example, a professor of medicine). A doctor need not be a man, but many doctors are men, and the same holds between professors and men. Because one and the same person can be a professor, a doctor, and a man all at once, the diagram needs all three circles to overlap with each other in pairs, plus one shared region where all three groups meet together.

• A diagram where one circle is drawn completely inside another forces a strict subset relationship, so every member of the smaller group would have to also be a member of the larger group - this is not true here, since professors, doctors and men are independent, non-hierarchical categories.

• A diagram where one circle is drawn entirely apart from the rest forces that category to share no members at all with the others - this is not true here, since a person can carry more than one of these descriptions.

• A diagram where each circle overlaps only its immediate neighbour, without any single region common to all three, forces every person to satisfy at most two of the three descriptions at once - this is not true here, since a person can be a professor, a doctor, and a man simultaneously.

The correct diagram is therefore the one where all three circles overlap each other in pairs and also share one common central region, capturing the fact that a person can be a professor, a doctor, and a man at the same time.