Study the following figure and answer the questions given below. How many…

Concept: In a numerical Venn diagram, each shape (rectangle, circle, triangle) stands for one category, and every number written inside a region is the count of people belonging to exactly the categories whose shapes overlap at that spot. To find how many belong to one category only, find the number that sits inside that shape but outside every other shape.

Application: Here the rectangle stands for Artists, the circle for Players and the triangle for Doctors. The number placed inside the rectangle but outside both the circle and the triangle is 30, so 30 people are artists but not players and not doctors.

Cross-check: None of the other regions is "rectangle only":

• 4 sits where the rectangle and circle overlap (artists who are also players).

• 8 sits where the rectangle and triangle overlap (artists who are also doctors).

• 3 sits where all three shapes overlap (artists, players and doctors together).

Only 30 sits inside the rectangle alone, confirming that 30 is the count of artists who are neither players nor doctors.