turing machine plzz xplain

Question

Let $A=\{\langle M\rangle \mid M$ is turing machine that halts on all inputs and $L(M)=L'$ for some undecidable language $L'\}$. Then $A$ is ____

a. Regular language
b. Recursive language but not regular
c. Recursively enumerable language but not recursive language
d. Non-recursively enumerable language

Comments

https://www.facebook.com/groups/core.cs/permalink/1078331485532437/

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regular

Answer 1

$M$ is a Turing machine that halts on all inputs implies L(M) is recursive.

Now, L(M) = L' for some undecidable language L'.

So, this means L(M) is an undecidable language.  But L(M) must be decidable as $M$ is halting on all inputs. So, there cannot be any such $M$ making $A = \emptyset$ which is a regular language.

Comments

so what is the answer to given question??

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Akriti sood 

The answer is option A which is regular language