Teachers in the middle ages supposedly tested the realtime propositional logic ability of a student using an obligato game. In an obligato game, a number of rounds is set and in each round the teacher gives the student successive assertions that the student must either accept or reject as they are given. When the student accepts an assertion, it is added as a commitment; when the student rejects an assertion, its negation is added as a commitment. The student passes the test if the consistency of all commitments is maintained throught the test.

1. Suppose that in a 3-round obligato game, the teacher gives the student the propositions p q r, followed by (p = q) r, and finally (r p) = q. For which of the eight possible sequences of three answers will the student pass the test?

2. Explain why every obligato game has a winning strategy.