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Question 501045: The police suspects that four persons hacked into the university computer
system. The four persons made the following statement to the police:
Anh: Phuong did it.
Phuong: Ben did it.
Tuan: I did not do it
Ben: Phuong lied when he said that I did it.
a. Suppose the police know that exactly one person is lying, who did it?
b. Suppose the police know that exactly one person is telling the truth,
who did it?
Justify your answer.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Only 1 Liar:
If A is the Liar, then both P and B must be telling the truth. But P and B made contradictory statements. A cannot be the Liar.
If P is the Liar, then A points the finger at P and this is not contradicted by assuming B and T were honest.
If T is the Liar, then again, P and B are contradictory. T cannot be the Liar.
If B is the Liar, then P and A are contradictory. B cannot be the Liar.
P did it.
One Truth Teller:
If A told the truth, P and B are again contradictory. A not the Truth Teller.
If P told the truth, then T must be lying, but B and T cannot both be the perpetrator, hence P is not the Truth Teller.
If T told the truth, then P and B are contradictory again. T is not the Truth Teller
If B told the truth, then A lied so P didn't do it and P lied so B didn't do it (which is what B said) and T lied and therefore T did it.
John
My calculator said it, I believe it, that settles it
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