A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded that:< a. If the butler is lying, then so is the handyman. b. The cook and the butler cannot both be telling the truth. (That is, it is not true that both the cook and the butler are telling the truth.) c. The cook and the gardener are not both lying. d. The butler is telling the truth only if the gardener is lying. - For each of the four witnesses, can the detective determine whether that person is telling the truth or lying? Use the truth table to explain your reasoning. Please use the following notations in your reasoning -- B: The butler is telling the truth. C: The cooking is telling the truth. G: The gardener is telling the truth. H: The handyman is telling the truth. e

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