Turing Recognizable Languages

Question

Okay , So R is RE , L is Regular language.

1) Definitely true , RE not closed under complement.

2) Regular union Non regular language ? Could be possbile. Not too sure.

3) L interesection R' is not RE ? Not sure

4) ?? Not sure

5) ?? Not sure 

Can you help with these ?

Answer 1

I think none of the option is correct.

A. RE are not closed under Complement operation. So it is not evern Turing Recognizable

B and C and E options. Since RE' is not even Turing Recognizable and we don't know anything about those languages. So we cannot comment on any operation on those Languages. Threrefore all are False.

D. LUR is Recursive Enumerable but not Recursive. To find the Union Move L to upper Level in Chomsky Hierarchy to RE languages. Since RE are closed under Union. Therefore LUR is RE and not Recursive. So this statement is also False.