In Washington, either party can end a tenancy on 20 day's notice so long as the notice is given to the other party more than 20 days before the end of the rental period. For example, if you got (or gave) a notice on April 10 that said you needed (or wanted) to be out April 30, that is a valid notice. A longer notice period is OK - 20 days is the shortest possible period.
Since they have all ready rented your apartment, sounds like it is too late to rescind. You can't cancel it because you all ready issued it. Hope this helps (even though I know this is not what you wanted to hear) Elizabeth Powell