Professor Z was killed by one of his four students, who was helped by another of the four. His students declared:

A: If B is guilty of something, then C must be innocent.
B: If A is innocent, then C must be guilty.
C: If B was the killer, then D must have had nothing to do with the crime.
D: I am innocent.

As everybody should know, guilty parties always lie, and innocent people always tell the truth. Who killed the professor, and who was his accomplice?

First, It's important to note that in propostional logic, any conditional statement with a false antecedent is considered true.

If A were guilty, then his statement is false so the antecedent must be true and the consequent false, but that would mean that both B & C are also gulity making too many killers, so A must in fact be innocent.

If B is innocent then C must be guilty, meaning his statement is false, but the antecedent of C's statement is false so his statement would be true therefore B can't be innocent.

Both A's and B's statements then leave C innocent and therefore D the remaining culprit.

Since C's statement must be true, and the consequent of his statement is false, the antecedent must also be false.  So B is the accomplice and D is the killer.

Posted by Galendir on 2004-03-21 16:23:57