You can and should claim them as dependents and claim the American Opportunity Credit.
They meet all the rules like you said; the rules for a parent to claim a college student are this:
- The student is under the age of 24 on Dec 31 of the tax year and;
- Is enrolled in an undergraduate program at an accredited institution and;
- Is a full time student for some part of 5 months during the year, and;
- the STUDENT did NOT provide more that 50% of the STUDENT’S support
They will not qualify for the Recovery Rebate Credit and they would not qualify for the American Opportunity Credit if they filed by themselves since they are your dependents.
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