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@Opus 17 - on #4,  it's even narrower than written for AOTC; LLC is a different matter

 

Students are not eligibile for the refundable portion of AOTC if a) they are under 24 and not living independently AND B ) they are not orphans (either parent is alive)  AND c) they file other than MFJ.  ... so 8 permulatations and  7 of then maintain eligibility for the refundable portion of AOTC.... assuming they are not claimed as a dependent by someone else (otherwise, no eligibility).- the 'can be claimed' doesn't matter in this case. 

 

Not sure where the $20,000 comes from.  If there is a tax liability, there is eligibility for both the non-refundable portion of AOTC as well as LLC.  (assuming not claimed by someone else).