There are three men in front of a jury, suspected for the theaft of a car. They testify as follows: Bob: Alan stole the car. Jack cannot be guilty: he was all the time with me at Mc Doe’s pub.
Alan: If Bob stole the car, then Jack helped him.
Jack: I was at home that night, you can ask my wife. I’m sure at least one of the others is guilty.
Express the testimony of each suspect as a propositional formula, trying to use the fewest propositions as possible.
Write a truth table for the three testimonies and use it to answer the following questions:
1. Are the three testimonies consistent?
2. The testimony of one of the suspects follows from that of another. Which from which?
3. Assuming everybody is innocent, who committed perjury?
4. Assuming all testimony is true, who is innocent and who is guilty?
5. Assuming that the innocent told the truth and the guilty told lies, who is innocent and who is guilty?