Tenant notified me today that they are leaving. Have a question

[Lou Migliaccio]

Hi everyone. So today at 9pm I received a email that the tenant was terminating their lease. They have been renting for a few years from me and we recently went month to month with the agreement that I receive 45 days notice. So, tomorrow the rent is due and she told me today that they are giving notice. Also she said they would like to move out Dec 11. Are they responsible for the entire month? Can they give that short of notice regarding termination and not paying the rent?