Which Venn diagram represents the statement “Some men are not great scientists”?

Concept

In a categorical Venn diagram, shading means that a region is empty, while a cross means that at least one member exists in that region.

The statement “Some A are not B” is existential: it requires at least one member inside A but outside B.

Application

1. Let one circle represent men and the other circle represent great scientists.

2. The phrase “some men” requires an existing member of the set of men.

3. The phrase “are not great scientists” places that member outside the overlap with great scientists.

4. Therefore, put a cross in the part of the men circle that excludes great scientists.

Cross-check and contrast

• Shading the overlap would assert that no men are great scientists.

• Shading the great-scientists-only region would assert that every great scientist is a man.

• Shading the men-only region would assert that every man is a great scientist.

• A cross in the men-only region directly represents the required existential member.

Hence, the required representation is the diagram with a cross in the men-only region.