Task 5. In class 5A, a survey was conducted on what fruits the students like. It turned out that 13 students like apples, 11 like plums, 15 like peaches, and 6 like melons. A student can like more than one fruit. Every student who likes plums also likes either apples or peaches (but not both at the same time). And every student who likes peaches also likes either plums or melons (but not both at the same time). What is the minimum number of people that can be in $5 A$? (20 points)
Answer: 22 people.

Solution. Estimate. Since 15 people like peaches and 6 people like melons, there are at least 9 people who like peaches but do not like melons. Then all these people like plums but do not like apples. Therefore, in addition to these people, there are at least 13 people who like apples. Thus, the total number of people is no less than 22.

Example. Suppose 6 people like melons, peaches, and apples, 9 people like plums and peaches, 2 people like plums and apples, and 5 people like only apples. It is easy to see that in this case, the total number of people is 22, and all other conditions of the problem are satisfied.

Criteria. Estimate - 10 points.

Example - 10 points.