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?
I'm sorry but i think i must be having a slow day...
The way i see it at the moment is that the problem has erroneous propositions and technically is illogical...and I need help to see where i'm going wrong...
i heartily concur that if B is one of the two guilty parties everything fits with the conclusions that D is the killer and B the accomplice...
But, if B is innocent - what follows is :-
a] C is guilty [according to B]
b] C could be guilty or innocent [according to A]
[as B is not guilty] but must be guilty as A & B are innocent.
if C is guilty he lies - in other words if B was the killer then d may have had something to do with the crime - But in this line of thinking B isn't the killer so D can be guilty or innocent -i.e. d's guilt or innocence is unknowable D says he's innocent which must be a lie so D is a guilty party
C's statement can still be valid in the lie form
and C and D can be the guilty parties...
In other words I think the whole puzzle is erroneous...
I also question the "propositional logic" stance that a false antecedent necessitates a true conclusion in a lie - it doesn't - the conclusion becomes unknowable because it is only identifiable with the "if and only if"
It's been 15 years since i taught logic so call me an utter idiot if i'm being one , but I think there's a real problem with this...
Think there's something wrong..
