I graduated in May 2021 and didn't go to school after that. I am considered a full time student in 2021?

Most likely, but it depends on your fact situation.

Full-time students include individuals who, during some part of each of five months (not necessarily consecutive) during the calendar year, are either:
 

• Enrolled at a school that has a regular teaching staff, course of study, and regularly enrolled body of students in attendance, or
• Taking an on-farm training course given by a school or state, county, or local government.

A student is a full-time student if they're enrolled for the number of hours or courses the school considers to be full time.

A school includes technical, trade, and mechanical schools, but it doesn't include on-the-job training courses, correspondence schools, or night schools.

You're considered to be a half-time student or more if you carried at least one-half the normal full-time workload. You need to be half-time for at least one academic period during 2021.

If you're not sure about your enrollment status, Box 8 of your Form 1098-T will tell you whether you were at least half-time for your course of study.

Simple answer: yes.  See details at the other answer.

Usually, the next question is: can my parents still claim me as a dependent?  Answer: Maybe.

Graduation year answer (written as if the parent asked the question)

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:

1. he is a full time student under 24 for at least 5 calendar months of the year (graduating in May usually means you meet the 5 month rule)
2. he did not provide more than 1/2 his own support  (scholarships are considered 3rd party support and not support provided by the student). 
3. lived with the parent (including time away at school) for more than half the year

So, it usually hinges on  "Did he provide more than 1/2 his own support in 2021.

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  (page 15)