A detective has interviewed four witnesses to a crime. From the stories of witne

Question

A detective has interviewed four witnesses to a crime. From the stories of witnesses the detective has conclude that the butler is the truth then so is the cook; the cook and the gardener cannot both be telling the truth; the gardenner and the handyman are not both lying; and if the handyman is telling the truth than the cook is lying. For each of the witnesses, can the detective determine wether that person is telling the truth or lying? Explain your reasoning.

a. If the butler is telling the truth, then so is the cook.
b. The cook and the gardener cannot both be telling the truth.
c. The gardener and the handyman are not both lying
d. If the handyman is telling the truth, then the cook is lying.

For each of the four witnesses, can the detective determine whether that person is telling the truth or lying?

Explanation / Answer

Lets work backwards d. If the handyman is telling the truth, then cook is lying. -opposing stories here, if the cook is lying then the butler is also lying. c. The gardener and the handyman are not both lying. -The gardener and handyman must both be telling the truth, because [hint b] the gardener is not telling the same truth as the cook, and the handyman's story also implements the cook. b. The cook and the gardener cannot both be telling the truth(related to in part c.) a.If the butler is telling the truth, then so is the cook. This means that the butler and the cook share the same story, and are either both telling the truth or both lying. But since the gardener and the handyman cannot both be lying, and both their stories implement the cook, then the cook is lying. This means that the butler is lying. Therefore the handyman and the gardener are both telling the truth. I believe that is the correct, but I answered that from inferences off the top of my head. Good luck!

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