Yes, if your school considered you a full time student then you were a full time student in 2020 for tax purposes.
For the Qualifying Child dependent rule, you must have been full time for parts of calendar months. Graduating in May, even May 1st, means you usually meet this rule.
You don't say why you're asking. It's usually about being claimed as a dependent. See additional reply for a discussion on that.
That particularly important this year, with stimulus $ on the table.
Under the CARES Act, if you are claimed, or qualify to be claimed, as a dependent on someone else’s return you cannot receive a stimulus check, in 2020. If you qualified as a dependent for 2019, but will not be for 2020, you will most likely get it in 2021, when you file a 2020 tax return.
Graduation year
If he/she was a student (under 24) for at least 5 months and lived with you for more than half the year, and did not provide more than 1/2 his own support for the whole year, you can still claim him. Be sure he knows you're claiming him, so he doesn't claim himself. He can only be claimed once. But, he can "file taxes" without claiming his own exemption.
The real question is who should be claiming him in this "transition" year to adulthood. You two have to agree on who is going to claim his exemption. Each should do their taxes both ways and see which way the family comes out best. Even then, you have to meet the rules. The rule is that a child of a taxpayer can still be a “Qualifying Child” dependent, regardless of his income, if:
So, it usually hinges on "Did he provide more than 1/2 his own support in 2019.
The support value of the home you provided is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants. IRS Publication 501 on page 20 has a worksheet that can be used to help with the support calculation. See: http://www.irs.gov/pub/irs-pdf/p501.pdf