State whether the following closure properties are TRUE OR FALSE. If TRUE give the proof, if FALSE give a counter-example:

1) If L* is not regular then L must be regular FALSE

2) If L* is regular then L must be non-regular FALSE

3) If L* is regular then L must also be regular FALSE

4) If L* is not regular then L must also be non-regular TRUE

5) If the complement of L is not regular, then L must be regular

6) If the complement of L is regular, then L could be non-regular

7) If the complement of L is regular, then L must also be regular

8) If the complement of L is regular, then L must be non-regular

I know the closure properties of regular languages:

Regular Languages are closed under Union

Regular Languages are closed under Intersection

Regular Languages are closed under Concatenation

Regular Languages are closed under Kleene Closure

Regular Languages are closed under complementation

Regular Languages are closed under set difference

Regular Languages are closed under reversal

Likewise, can you give the closure properties of non-regular languages?