# 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.

Example:

, which is not CF

**If is CF, is regular. Then is CF, is CF.**

Why?

**If L is Context-free, then is also context free.**

You could just convert L into CNF, then switch the sequence.