# Complement of CFL is Recursive

If CFL are not closed under complementation, it means that if a language '$L$' is CFL then its compliment $L^C$ is not CFL. Then how can we discuss about $L^C$ being recursive?

My doubt arose because I think if a language cannot be decided CFL or not then how can it be declared Recursive ?

• CFL not being closed under complementation does not mean that a 'L' being in CFL means that it's complement is not in CFL. It just means that there exists an 'L' in CFL such that it's complement is not in CFL. Nov 9 '16 at 21:08

Therefore, if a language $L$ is CFL then it is also recursive and hence, $L^C$ is also recursive.