Who Killed Sharky in the Underworld Mystery?

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Sharky, the underworld leader, was killed by one of his four henchmen, and Detective Sharp determined that only one of their statements was true. Analyzing the statements reveals contradictions when assuming each one is true, leading to confusion about who the actual killer is. The discussions suggest that if Socko or Fats were telling the truth, it would imply multiple killers, which is impossible. Ultimately, reasoning points to Muscles as the likely killer, despite the complexities in the statements. The conclusion drawn is that Muscles is the one who killed Sharky.
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Sharky , a leader of the underworld , was killed by one of his own band of four henchmen . Detective Sharp interviewed the men and determined that all were lying except for one. He deduced who killed Shark on the basis of the following statements :

a) Socko: Lefty Killed Sharky
b) Fats: Muscles didnt kill Sharky
c) Lefty: Muscles was shooting craps with Socko when Sharky was knocked off
d) Muscles: Lefty didnt kill Sharky

who did kill Sharky?
 
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Go through each of the four statements, assuming that that one is correct and the others incorrect. Here's #1:
By a, Lefty Killed Sharky. By b, Muscles killed Sharky; contradiction.

So a is lying.
 
i do it like this..
first i negation all of the statements
second Then i check it 1 by 1 see whether got contradiction a not(like what u had done)
third if there r a contradiction occurs , i will ignore it and go for the next.
last i found that it was Muscle who did kill Sharky

Is it like this?? My logic sense is quite poor..~ hehe
 
The question appears to be inconsistent.
1/ One of (a) or (d) must be true (because one statement is the complement of other)
2/ Similarly, one of (b) and (c) must be true.
Therefore, we find two true statement maker {one from (a) or (d) and the other from (b) or (c)}.
Thus the condition of the question that 'only one is stating the truth' does not hold good.
 
RyozKidz said:
Sharky , a leader of the underworld , was killed by one of his own band of four henchmen . Detective Sharp interviewed the men and determined that all were lying except for one. He deduced who killed Shark on the basis of the following statements :

a) Socko: Lefty Killed Sharky
b) Fats: Muscles didnt kill Sharky
c) Lefty: Muscles was shooting craps with Socko when Sharky was knocked off
d) Muscles: Lefty didnt kill Sharky

who did kill Sharky?

I think the question is fine, we have 4 cases to consider.

CASE 1: Socko is the one telling the truth. Then Lefty killed Sharky is the truth. But if Socko is the only one telling the truth, then the others must be lying. So Fats (who is lying) says that muscles didn't kill Sharky, ...thus Muscles DID kill Sharky. Two different people killed Sharky? Not possible...thus case 1 is ruled out.

CASE 2: Fats is the one telling the truth. So Socko, Lefty and Muscles are lying.

So we deduce from Socko's lying statement that...Lefty did not kill Sharky.

We deduce from Fats' true statement that...Muscles did not kill Sharky.

We deduce from Muscles lying statement that...Lefty did kill Sharky.

So Lefty did kill him, but also did not? That's a contradiction. So either case 3 or 4 is true. But you can figure using reasoning that one of them cannot happen...just like I did here.

CASE 3: 4 u
CASE 4: 4 u
 
Wow..~ But i deduced tat is Muscle who did kill Sharky..T_T''
 
I'm taking a look at intuitionistic propositional logic (IPL). Basically it exclude Double Negation Elimination (DNE) from the set of axiom schemas replacing it with Ex falso quodlibet: ⊥ → p for any proposition p (including both atomic and composite propositions). In IPL, for instance, the Law of Excluded Middle (LEM) p ∨ ¬p is no longer a theorem. My question: aside from the logic formal perspective, is IPL supposed to model/address some specific "kind of world" ? Thanks.
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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