As your son is under 24 and a full-time student, you can claim him as a dependent if he did not provide for more than half of his own support. The test is to be done for the full year.
This test is different from the one requiring you to provide more than half of his support.
As for his rent, if he actually paid it, it is counted as him paying it even if you are co-signers.
Please read this TurboTax Help topic for more information.
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