2.4 CFL Properties
If and are context-free languages, then so are:
You could genertate new Grammars to prove them easily.
But the intersection of two CFL are not necessary Context-free.
Because a stack cannot record the actions of pop and push from two CF languages at the same time.
, which is not CF
If is CF, is regular. Then is CF, is CF.
If L is Context-free, then is also context free.
You could just convert L into CNF, then switch the sequence.