IRS Publication 501
discusses dependent exemptions
It's tough to provide the cliff notes version because the IRS publications are
the "cliff notes versions" of the actual law, which is codified in Chapter 26 of the U.S. Code, commonly referred to as "the tax code". (In fairness, if you have ever seen the real cliff notes, you would probably agree that it would be nice if there were cliff notes to cliff notes.)
The extra, super short, incomplete overview is that non-minor children can be claimed if:
1. they are a member of the household for the entire year if they do not have a special relationship (e.g. step-parent or adult child) or
they have a special relationship and live with you for at least 1/2 the year;
2. their income is less than $3,650;
3. the person claiming the person provided for more than half their support for the calendar year.
I hope that this helps you to understand the law in your situation. Let me know if I may be of further assistance. Thank you.