The region which represents artists who are neither sportsmen nor professors.

Concept

In a Venn diagram, each circle is the set of all members of one category. Every lettered region is fixed by which circles it lies inside: a point belongs to a category when it lies inside that category's circle, and does not belong when it lies outside that circle.

So a description of the form "X who are neither Y nor Z" always names a single region — the part that lies inside the X circle while lying outside both the Y circle and the Z circle.

Application

Here circle A is Artists, circle P is Professors and circle S is Sportspersons. The set asked for is: inside A, outside S, outside P.

1. Start with the whole of circle A, which holds every artist.

2. Remove the part of circle A that overlaps circle S, because those artists are sportspersons as well.

3. Remove the part of circle A that overlaps circle P, because those artists are professors as well.

4. What remains is the crescent of circle A lying outside both other circles, and that region is lettered e.

Cross-check

Testing the other lettered regions against the two exclusions confirms the reading:

• b lies inside A and S, so its members are artists who are also sportspersons, which the phrase "neither sportsmen" rules out.

• g lies inside A and P, so its members are artists who are also professors, which the phrase "nor professors" rules out.

• a lies inside all three circles, so its members are artists who are both sportspersons and professors.

• d lies inside S alone, so its members are sportspersons and not artists at all.

Result

The region standing for artists who are neither sportsmen nor professors is e.