## Task 1 - 300721

The following statements are made about the students in a class:

(1) Exactly 10 students are members of a working group.

(2) Exactly 8 students are members of a sports group.

(3) Exactly 5 students are neither members of a working group nor a sports group.

Give the

a) smallest possible,

b) largest possible

number of students in the class for which the three statements can be true! Justify your answers!
a) To obtain the smallest possible number, one chooses the option that two of the three statements apply to as many students as possible.

This means: Exactly 8 students belong to both a working group and a sports group.

Then it follows: Exactly 2 students belong to a working group but not to a sports group. Together with the 5 students mentioned in (3), this results in $8+2+5=15$ students.

b) To obtain the largest possible number, one chooses the option that two of the three statements apply to (as few as possible, i.e.,) none of the students. This results in a total of $10+8+5=23$ students with the students mentioned in (1), (2), and (3).