## Task 1 - 120611

In a class of 30 students, 20 students regularly read the magazine "Fröhlichsein und Singen" (Frösi), 12 students read the mathematical student magazine "alpha", and 6 students read neither "Frösi" nor "alpha".

Determine the number of all students in this class who read both magazines!
Let the number of students who read both magazines be $x$.

Then exactly $(20-x)$ students read "Frösi" but not "alpha", and exactly $(12-x)$ students read "alpha" but not "Frösi". Therefore, we have

$$
x+(20-x)+(12-x)+6=30
$$

which simplifies to $38-x=30$, hence $x=8$.