## Task 1 - 270621

In a 100 m race that the three students Jens, Michael, and Peter participated in, the following predictions were made:

Frank said: "Jens or Peter will win."

Horst said: "If Jens does not win, then Michael will win."

Norbert said: "If Michael wins, then Jens will be second."

Stefan said: "Michael will perform worse than Jens and Peter."

(a) After the race, it was found: All four predictions are true statements.

(b) After the race, it was found: Horst was the only one who made a true statement.

In both cases (a), (b), state who came in first, second, and third! In both cases (a), (b), it is known that Jens, Peter, and Michael all ran different times.

Explain how you arrived at your answers!
(a) According to Stefan's statement, Michael came in third. Jens must have won; otherwise, Horst's prediction would result in the false statement that Michael won. So Jens came in first and Peter second.

(b) Since Frank's statement was false, Michael won. Therefore, and because Norbert's statement was false, Jens could not have come in second; consequently, he came in third and Peter second.