Which of the following diagrams best indicates the relationship between Tall…

When three categories can each overlap with the other two - that is, no category is entirely contained in another, and no category is completely separate from another - the diagram that correctly represents every possible combination is three circles that all mutually intersect, so a region exists for people belonging to any one, any two, or all three categories.

Here, 'tall men', 'black-haired people', and 'Indians' are three independent traits: a person can be tall without being Indian, black-haired without being tall, Indian without being either, or any combination of all three. Since none of the three groups is a subset of another and none excludes another, the diagram must show all three circles overlapping each other, exactly as in the diagram with three mutually intersecting circles labelled Tall men, Black haired people, and Indians.

Comparing with the other diagrams confirms this:

• A diagram that nests one circle fully inside a larger circle and draws a third circle completely apart from both wrongly forces one trait to be a subset of another while keeping the third trait from ever overlapping with either - that does not match these three independent, overlapping traits.

• A diagram that nests all three circles strictly inside one another wrongly forces a hierarchy (innermost inside middle inside outermost), which would require every Indian to be black-haired and every black-haired person to be tall - not something these categories imply.

• A diagram with two overlapping circles fully enclosed within a third, larger circle wrongly forces everyone in either of the two overlapping groups to also belong to the third group - again not implied by these independent traits.

So the diagram with three mutually overlapping circles is the correct representation.