They both receive the standard deduction whether you claim them or not. You do not have to claim either one of them.
They both have to indicate whether or not they can be claimed by someone else (you) or not. They can both file their own tax returns and you not claim either of them. You eldest child can only claim the American Opportunity Tax Credit if he is not claimed on your return.
How do I answer the "Did you support yourself in 2019?" question? Did I support myself?
You can start as many tax returns as you like which you should do to see your options. Choose the option that is most beneficial to your family. Make sure that you keep the user IDs and passwords as it can get confusing when working with multiple returns.
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