Yes. A full-time student for tax purposes is someone who meets the full-time requirements of their school for at least part of the month for five months, which do not have to be consecutive.
@shaun-epaints and just to add, that is any part of 5 months in the same calendar year - so for 2021, you have 5 months, even though August is just 2 days.
if you only attended school from Sept, 2021 through January 2022, you would not be a full time student in either 2021 or 2022.
IRS publication 970 / page 22:
Full-time student. You are a full-time student for 2021 if during any part of any 5 calendar months during the year you were enrolled as a full-time student at an eligible edu-cational institution (defined earlier), or took a full-time, on-farm training course given by such an institution or by a state, county, or local government agency.