Women Or Tigers? — The Second Challenge

So the first prisoner who was subject to the eccentric king’s new scheme not only saved his life but could even leave the arena with a lovely wife.

The king now changed the signs on the two doors and chose new tennants for the rooms behind them. The signs now read:

ROOM I: THERE IS A WOMAN IN AT LEAST ONE OF THE ROOMS

ROOM II: THERE IS A TIGER IN THE OTHER ROOM

‘Are the signs telling the truth?’, asked this second day’s prisoner.
‘Either they are both true or they both tell a lie’, was the king’s reply.

Which room should the prisoner pick?