Answer :
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.
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.