It's possible. Capitalization is for emphasis and importance.
If the student:
-was under the age of 24 on Dec 31 of the tax year.
-was enrolled as a full time student for *any* *one* semester that started in the tax year and:
-Was a student for at least 5 months of the tax year and:
-The ***STUDENT*** did ***NOT*** provide more than 50% of ***THEIR OWN*** support for the ***ENTIRE*** year. and
-was enrolled in a course of student that leads to a degree or credentialed certification and
-was an *UNDER*graduate on ***JAN 1*** of the tax year, then:
The parents qualify to claim the student as a dependent. The student must select the option for "I can be claimed on someone else's return" on the students tax return, if the student is required to file their own tax return.
Now the key word here is ***QUALIFY***. It does not matter if the parents claim the student or not. If the parents ***QUALIFY*** to claim the student, then the student must select the option for "I can be claimed on someone else's tax return" regardless of if the parents claim the student or not.
If May 1st was the graduation date, then the *ENTIRE MONTH* of May counts of one of the 5 months the student was enrolled.
Note that all six of the above requirements must be met for the student to qualify to be claimed as a dependent on the parent's tax return.
