Suppose a prisoner must make a choice between two doors. One door leads to freedom and the other door is booby-trapped so that it leads to death. The doors are labeled as follows:

Door 1: This door leads to freedom and the other door leads to death.

Door 2: One of these doors leads to freedom and the other of these doors leads to death.

If exactly one of the signs is true, which door should the prisoner choose? Give reasons for your answer.