[Original]
Seafrog
2004-09-01 This article is an article that I am studying by the discrete mathematics class. This article comes from a question in my homework:
A logicalist misuses a tribe, which is imprisoned in prison, and he said to the logician: "There are two doors today, one is free, one is death, you can open one. Now from two One person chooses one person to answer any of the questions you mentioned (Y / N), one of which is honest, one person is lying into a sex, life is dead, you will choose. "Logicist thinking, asking a warrior, then Open the door. How should logic be asked?
This article conducts detailed analysis of this issue, hoping to provide some ideas for the solution of friends to solve the logic problem.
Author: Zhou Xiang
The "Discrete Mathematics (below)" textbook in the Mountain Monetal Computer College has such a question:
A logicalist misuses a tribe, which is imprisoned in prison, and he said to the logician: "There are two doors today, one is free, one is death, you can open one. Now from two One person chooses one person to answer any of the questions you mentioned (Y / N), one of which is honest, one person is lying into a sex, life is dead, you will choose. "Logicist thinking, asking a warrior, then Open the door. How should logic be asked?
A reasonable answer should be like this: the logistician pointed to a question, no matter what he asked is honest or lying, if this door is the door to the free door, if it is the door of death Repay. For questions about the warriors, you can include two simple propositions, you might as well, to symbolize these two simple propositions:
P: This door is the door of freedom; Q: You are honest
There are 4 combinations for these two propositions:
Pq
0 0
0 1
1 0
1 1
The answer symbolize the warrior: A: The warrior's answer
If the logical person refers to the door of the free door, P = 1, no matter what he asks is honest or lying, there is always a = 1
If the door of the logic means is not the free door, P = 0, no matter what he asks is honest or lying, there is always a = 0
That is, four combinations above,
P q a
0 0 0
0 1 0
1 0 1
1 1 1
Considering that the answer when Q = 0 is fake, the true value of the actual atomic proposition should be:
P q a
0 0 1
0 1 0
1 0 0
1 1 1
This is very clear, recalling the five basic logic relationships: non-, unpaid, extract, implication, and equivalent truth table, we found that only the equivalent truth table is the same as the above table, Therefore, the answer is:
Logic people should ask:
P ← → Q?
That is, the problem should be asked: "The proposition P is equivalent to the proposition Q is the true life?" Or "I refer to the door is true and only when you are honest?")
Of course, ask him to ask him in the tribe, you may not understand, the logicalist doesn't know what to do. Maybe you can also ask the language to help :)
