Which region represents professors who are also sportspersons but are not…

Concept

In a Venn diagram, each circle represents a set, and an overlap represents members common to the corresponding sets.

A condition such as ‘in P and S but not in A’ means taking the intersection of P and S and then excluding every point that lies in A.

Application

1. Let A, P and S denote the sets of artists, professors and sportspersons, respectively.

2. ‘Professors who are also sportspersons’ gives the intersection P ∩ S.

3. ‘But not artists’ removes the part inside A, so the required set is (P ∩ S) \ A.

4. In the given diagram, the region representing (P ∩ S) \ A is labeled c.

Contrast

• Region e lies only inside A, so it represents artists who are neither professors nor sportspersons.

• Region f lies only inside P, so it represents professors who are neither artists nor sportspersons.

• Region g lies inside A and P but outside S, so it represents artist-professors who are not sportspersons.

Cross-check

Region c is inside both P and S and outside A, so it satisfies all three membership conditions.

Therefore, the required region is c.