The exercise is a puzzle that can be solved by translating Statements into logical expressions and reasoning from these expressions using truth tables.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 both 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? Explain your reasoning.

Solution: Step 1 ; A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has concluded that:1. If the butler is telling the truth, it refer as (b), then so is the cook, it refer as (c) .2. The cook(c) and the gardener(g) cannot( both be telling the truth. (c) The gardener(g) and the handyman(h) are not( both lying. (d) If the handyman(h) is telling the truth then the cook(c) is lying).Step 2 ; First we should translate this statement to logical expression.Assume that b indicate butler, c indicate cook, g indicate gardner and h indicate handyman.Translated expressions are (a) (b) (c)(d) Truth table :bcghFFTT TFFTT TFFFT T