It depends. If your adult son receives $4500 in taxable income (W2 wages or a 1099-R, for example), you can't claim him. However, if his child (and he) live with you, you can claim his child as a dependent as long as he chooses not to. (A biological parent has a priority claim over another relative such as a grandparent).
If your adult son received Social Security income , or another form of, nonreportable disability, then you may claim him also if you provided at least half of his financial support.
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