Good-for-nothing Prosecutor

Logic Level 2

Three men X, Y, and Z were tried for breaking and entering. It is known that the prosecuting attorney either always lies or always tell the truth. He made the following statements in court:

(1) X is not guilty.
(2) Either Y or Z are guilty.
(3) Z is guilty.

One person who is guilty. Who is definitely not guilty?

Not enough info Y X Z

1 solution

Brian Charlesworth
Jan 19, 2016

If the attorney is always telling the truth, then the three statements are consistent with $Z$ being guilty and both $X$ and $Y$ being innocent.

If the attorney is always lying, then the three statements are consistent with $X$ being guilty and both $Y$ and $Z$ being innocent.

Since only $Y$ is innocent in both scenarios, we can conclude that $Y$ is definitely not guilty regardless of the veracity of the prosecutor. (The jury is still out regarding $X$ and $Z$ .)

Actually in the truth case Y could be guilty, because "Either Y or Z are guilty" does not mean if Z guilty then Y is innocent, both of them could be guilty.

But I think in common sense and add an assumption that only one person are guilty

Tran Hieu - 5 years, 4 months ago

Good point. If the attorney is telling the truth then $Y$ could still be guilty, (If the attorney is lying then $X$ is guilty, $Z$ is not guilty and in order for statement (2) to be a lie $Y$ would also have to be not guilty.) So I think that you're correct in pointing out that the question should specify that only one person is actually guilty.

@Chung Kevin I think Tran Hieu is correct in suggesting that the question should specify that precisely one person is actually guilty in order for the answer to unambiguously be $Y$ .

Brian Charlesworth - 5 years, 4 months ago

@Tran Hieu @Brian Charlesworth thanks guys, I failed to spot this ambiguity. I've updated it!

Chung Kevin - 5 years, 4 months ago

Good-for-nothing Prosecutor

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