"The prisoner is presented with two doors. In a room behind each door is either gold or a tiger. The sign on the doors are either both true or both are false.

Door 1: Either there is a tiger behind this door or gold behind the second door.

Door 2: There is gold behind this door.

Which door should the prisoner open?"

I have been trying to figure out the answer to this question. If I interpret Sign 1 as an inclusive or, then I end up getting 3 "no contradiction" cases, but it doesn't tell me which Door is the best choice (unless we actually care about probability such as 2/3 chance of getting Gold). To mitigate this, the best I could come up with is to interpret Sign 1 as an exclusive or.

[Solution attempt](https://i.stack.imgur.com/1GfpJ.jpg)

EDIT: Here are other places on the internet where the same problem appears.

<http://pi.math.cornell.edu/~araymer/Puzzle/PuzzleNights.html>

(Page 4) <http://www2.gcc.edu/dept/math/faculty/BancroftED/teaching/handouts/MATH213_rules_of_inference.pdf>

<https://www.ibtimes.co.uk/mathematician-puzzle-maker-raymond-smullyan-dead-97-1605912>