TURING MACHINE

Question

is every SEMI DECIDABLE an RE but not RECURSIVE??

plz help me with this.

Comments

RE(but not recursive) itself means Semi Decidable. Means TM can decide only its yes instances.
If TM can decide No instances as well, which means the language is decidable(Recursive).

Answer 1

For a language $L$

If there is some Turing Machine that accepts every string in $L$ and rejects every string not in $L$, then $L$ is a decidable language.

if there is some Turing machine that accepts every string in $L$ and either rejects or loops on every string not in $L$, then $L$ is Semi-decidable or recursive enumerable(RE)  or computably enumerable (CE).

Semi-decidable means "Recursive enumerable".

Undecidable means "Not REC"

Semi-Decidable And Undecidable means "RE but Not REC"

Answer 2

I hope,the concept is clear .

Comments

I have mentioned nowhere that semi decidable is a subset or superset of undecidable. I have just shown the relation between decidable and semi decidable problem. "semi-decidable as a subset of undecidable is technically wrong" is correct .

This is the relation between the three types if I am not wrong.

---

Yes, that relationship is correct. But in your answer the third column heading should be "not even semi-decidable" and not "undecidable".

---

OK.