Turing Machine and Recursive Enumerable Language

Question

If L and Ľ both are recursive enumerable language, then why L is recursive language?

Comments

Recursive languages are closed under complementation. Hence if L is recursive then L' also become recursive and every recursive language is recursive enumerable language.

If L is recursively enumerable then L' may or may not be recursively enumerable, recursively enumerable languages are not closed under complementation, hence we can't say L is recursively enumerable language.

Answer 1

Let M1 be the recognizer for L

Let M2 be the recognizer for L'

Run M1 and M2 in parallel , x(any arbitrary string) will either belong to M1 or M2.

So , either M1 or M2 will halt and one of them wil accept x

if M1 accept then accept and if M2 accept then reject

Either ways u will eventually halt with a decision and thus  L will be recursive language.........