It is well-known that regular languages are closed under the following operations: union, complement, and intersection. It is also well-known that all finite languages are regular. For each of the...

It is well-known that regular languages are closed under the following operations: union, complement, and intersection. It is also well-known that all finite languages are regular. For each of the operations, union, intersection and complement, are finite languages closed under them? If yes, prove it. Else provide couter examples.