When Socrates was imprisoned for being a disturbing influence, he was held in high esteem by his guards. All four of them hoped that something would occur that would facilitate his escape. One evening, the guard who was on duty intentionally left the cell door open so that Socrates could leave. Socrates did not attempt to escape but the open door was considered by the authorities to be a serious breach of security. It is unclear who was on duty that evening. In the testimony of the investigation, each guard makes two statements: A: 1. I did not leave the door open. 2.C was the one who did it. B: 1. I was not the one on duty that evening. 2. A was on duty. C: 1. B was the one who was on duty that evening. 2. I hoped Socrates would escape. D: 1. I did not leave the door open. 2. I am not surprised that Socrates did not try to escape. Assuming that one of the guards is guilty and that exactly three statements are true and the other five are false, deduce which of the guards left the door open. Given the fact that the guards make a total of eight utterances, a truth-table analysis of this problem is potentially very large. Fortunately, many of the distinct statements express the same proposition, and only five distinct propositions are involved. Also, the assumption about the total number of true and false statements further simplifies the problem. Note that it may not be directly deducible from the testimony whether a given statement is true or false. Guilty A.1 A.2 B. 1 B.2 C.1 C.2 D.1 D.2 A B C D

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