A detective has interviewed four witnesses to the crime. From the stories of witnesses the detective has concluded that :
(a) If the butler is telling the truth, then the cook is lying.
(b) If the handyman is lying, then so is the butler.
(c) Exactly one of the cook and the gardener are telling the truth
(d) The handyman and the gardener are not both telling thr truth.
For each of the four witnesses, can the detective determine whether that person is telling the truth or lying? Explain your reasoning.