The problem describes the exercise preferences of people in a locality. 25 people like walking, 22 like running, and 15 like cycling. We are also given the number of people who like combinations of these activities: 11 like walking and running, 9 like running and cycling, 7 like walking and cycling, and 3 like all three. 7 people do not like any of the activities. The task is to draw a Venn diagram to represent this information.

1. Problem Description

The problem describes the exercise preferences of people in a locality. 25 people like walking, 22 like running, and 15 like cycling. We are also given the number of people who like combinations of these activities: 11 like walking and running, 9 like running and cycling, 7 like walking and cycling, and 3 like all three. 7 people do not like any of the activities. The task is to draw a Venn diagram to represent this information.

2. Solution Steps

To construct the Venn diagram, we work from the innermost intersection outwards. Let W, R, and C represent the sets of people who like walking, running, and cycling, respectively.

* $W \cap R \cap C$: 3 people like all three activities. Place '3' in the intersection of all three circles.

* $W \cap R$: 11 people like both walking and running. Since 3 already like all three, $11 - 3 = 8$ people like only walking and running. Place '8' in the intersection of W and R, outside the intersection with C.

* $R \cap C$: 9 people like both running and cycling. Since 3 already like all three, $9 - 3 = 6$ people like only running and cycling. Place '6' in the intersection of R and C, outside the intersection with W.

* $W \cap C$: 7 people like both walking and cycling. Since 3 already like all three, $7 - 3 = 4$ people like only walking and cycling. Place '4' in the intersection of W and C, outside the intersection with R.

* W: 25 people like walking. Of these, 8 like walking and running only, 4 like walking and cycling only, and 3 like all three. So, $25 - 8 - 4 - 3 = 10$ people like only walking. Place '10' in the W circle, outside all intersections.

* R: 22 people like running. Of these, 8 like walking and running only, 6 like running and cycling only, and 3 like all three. So, $22 - 8 - 6 - 3 = 5$ people like only running. Place '5' in the R circle, outside all intersections.

* C: 15 people like cycling. Of these, 4 like walking and cycling only, 6 like running and cycling only, and 3 like all three. So, $15 - 4 - 6 - 3 = 2$ people like only cycling. Place '2' in the C circle, outside all intersections.

* Outside all circles: 7 people do not like any of the activities. Place '7' outside all circles.

3. Final Answer

The Venn diagram has three overlapping circles representing W, R, and C. The values placed in each region are as follows:

* $W \cap R \cap C$: 3

* $W \cap R$ (only): 8

* $R \cap C$ (only): 6

* $W \cap C$ (only): 4

* W (only): 10

* R (only): 5

* C (only): 2

* Outside all circles: 7