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A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded that if the butler is telling the truth then so is the cook; the cook and the gardener cannot be be telling the truth, the gardener and the handyman are not both lying; and 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?

Can some help me to solve this problem using Mathematical Logic? No need to put it into prolog. I spent 6.5 hours so far trying and had to give up.

-Shahabudeen