True or False. Briefly explain.

1) If L is context free, then L L must also be context free.

2) If L is context free, then L L must be regular.

3) If L is context free, then L must also be context free.

4) If L₁ L₂ and L₂ is context-free, then L₁ must also be context-free.

5)The context-free languages are closed under concatenation with the regular languages.

6) The regular languages are closed under union with the context-free languages.