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Yes, you can claim both of them as a dependents.

Here is standard by which you will be claiming him and his mother:

·       You provided more than half of their support.

·       They made less than $4,150 in gross taxable income. 

·       They lived with you for the entire year if non relative.

·       They are not a dependent on someone else’s taxes.

·       They are not filing a joint return with someone else.

·       They are a U.S. citizen, resident alien, national, or a Canadian or Mexican resident. 

For more information, follow this link: Turbo Tax on Dependents

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