Give a Context Free Language, is the complement of this language always recursive(REC)?
We have $\text{CFL} \subset \text{R} \subset \text{RE}$. As you have mentioned, $\text{RE}$ is not closed under complementation, but $\text{R}$ is. Hence, the complement of a CFL is also in $\text{R}$ (though not necessarily another CFL).