Question

A king tried his political prisoners based on Frank Stockton’s story “The Lady or the Dragon’. The prisoner must choose one of two doors. Behind each door is a room containing either a lady or a dragon. It is possible that both rooms contain ladies or that both rooms contain dragons, or that one room contains a lady and the other room contains a dragon. If the prisoner chooses the room with the lady, he goes free. If he chooses the room with the dragon, he is eaten. There is a sign on each door. The king tells the prisoner that the signs on the door are either both true or both false. The sign on door #1 says “At least one of these rooms contains a lady”. The sign on door #2 says “A dragon is in the other room.” Which room should the prisoner pick?

Answer 1

If both statements are true 
Room 1 = Tiger and Room 2 = Lady 
If both statements are false 
According to sign on room 1 
Room 1 = Tiger and Room 2 = Tiger 
According to sign on room 2 
Room 1 = Lady and Room 2 = Unknown 
So for the false case there is a disagreement between the signs. Therefore both signs must be true. 
He should chose room 2.