Can you be eligible for the EIC and child expense credit if the other parent is claiming the child?

Hello! I had a baby in 2018, and his father will be claiming him this year on his taxes. When filing my personal taxes (we are not married but live together), TurboTax asked me if I or the other parent would be claiming him. I checked that the other parent would be claiming him, but TurboTax tells me I still qualify for the EIC (my AGI for 2018 was $21,000), and for the childcare expense credit. Is this the truth? I just want to make sure I’m entering information correct and this is confusing me! 


Thanks 🙂