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?

(In reply to re: solution by e.g.)

e.g. is correct. 

"If I won the lottery last week, I have a lot of money today" is a true statement. But "I won the lottery last week" can be false, and "I have a lot of money today" can still be true.

But if you replace "if" with "if and only if", then the falseness of the antecedent does imply the falseness of the consequent.

If I were bitten by a rabid dog, I would say "I will survive if and only if I get the rabies vaccine". Then if I don't get the rabies vaccine [the antecedent is false], I will not survive [the consequent is false].

 

Posted by Penny on 2004-03-09 16:39:43