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39. A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has con- cluded 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 ly- ing; and if the handyman is telling the truth then the cook is lying. For each of the four witnesses, can the detec- tive determine whether that person is telling the truth or lying? Explain your reasoning.

39. A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has con- cluded 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 ly- ing; and if the handyman is telling the truth then the cook is lying. For each of the four witnesses, can the detec- tive determine whether that person is telling the truth or lying? Explain your reasoning.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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puzzles that can be solved by translating
statements into logical expressions and reasoning from these
expressions using truth tables.

39. A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has con- cluded 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 ly- ing; and if the handyman is telling the truth then the cook is lying. For each of the four witnesses, can the detec- tive determine whether that person is telling the truth or lying? Explain your reasoning.
Transcribed Image Text:39. A detective has interviewed four witnesses to a crime. From the stories of the witnesses the detective has con- cluded 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 ly- ing; and if the handyman is telling the truth then the cook is lying. For each of the four witnesses, can the detec- tive determine whether that person is telling the truth or lying? Explain your reasoning.
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