If you are asking whether the law requires him to abide by the dates in your letter, he does not. He could have legally accepted your resignation effective December 2, if he chose to.
He is not required by law to pay you beyond the last day you actually work. However, if he does not pay you for the unworked notice period, it is possible that you may qualify for unemployment for the period between 12-16 and 1-4. It can't hurt to apply; the worst they can say is no.

