## Task 2 - 270722

Angela, Bodo, Constanze, and Dietmar are discussing the outcomes of two football matches between class 7a and class 7b. For both matches, they make the same statements, namely:

Angela: The match ended in a draw.

Bodo: Class 7a won.

Constanze: Bodo's statement is false.

Dietmar: Angela's statement is true.

(a) Petra, who saw the first match, truthfully states that for the first match, exactly one of the four statements is false.

(b) Rolf, who saw the second match, truthfully states that for the second match, exactly one of the four statements is true.

Investigate whether (a) from Petra's statement, (b) from Rolf's statement, the outcome of the respective match (win for 7a, win for 7b, or draw) can be uniquely determined!
(a) If Dietmar's statement were false, then Angela's statement would also be false. However, according to Petra's observation, only exactly one statement is false, which clearly implies that Dietmar's and thus Angela's statement is true.

This clearly implies: The first game ended in a draw.

(b) If class 7a won the second game, then Bodo's statement is true and consequently Constanze's statement is false; furthermore, Angela's and thus also Dietmar's statement would be false.

If class 7b won the second game, then Bodo's statement is false and consequently Constanze's statement is true; furthermore, Angela's and thus also Dietmar's statement would be false.

Since there are thus two different outcomes of the second game where Rolf's observation holds true, the outcome of the second game cannot be uniquely determined from this observation.