A few questions that aroused while I was solving past midterms:

1. Prefix

A(l1,l2)={X | there's Y that belongs to l1 and XY that belongs to l2}

so if l2 is regular so is A(l1,l2) with no regard to l1. why is that?

2. Why is the language below not a CFL and its complement is.. How do you calculate its complement with a PDA?

L={uv | |u|=|v| for every i u(i)!=v(i) }

3. Let L be a CFL and R be a regular Language.

why is R/L has to be regular ?

4. why for every infinite CFL there's a sub-language which is also infinite and a CFL ?

Thanks!