# Two Turing machines M1 and M2 with \$ L (M1) subseteq L (M2) \$

Suppose M1 and M2 are two Turing machines $$L (M1) subsetsq L (M2)$$, Then

(A) M2 will not stop at any input where M1 does not stop

(B) M2 stops at each input where M1 stops

(C) At each input that M1 accepts, M2 stops.

(D) At each input that M2 accepts, M1 stops.

I am confused between B and C. This was an online test question.

For (B) my assertion is that if M1 can determine the language (M1 stops at each input), then since this is given $$L (M1) subsetsq L (M2)$$M2 should also be able to stop and decide on every input.

Option (C), however, looks convincing. If for each input M1 is in the language "yes", M2 should be able to decide also for this input.

Please let me know how I can handle this correctly.