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

Suppose that M1 and M2 are two Turing machines such that $$L (M1) subseteq L (M2)$$. then

(A) On each entry on which M1 does not stop, M2 does not stop

(B) On each entry on which M1 stops, M2 also stops

(C) On each entry accepted by M1, M2 stops.

(D) On each entry accepted by M2, M1 stops.

I am confused between B and C. It was a question of practice testing online.

For (B), I assert that when M1 is able to choose the language (M1 stops on each entry), then, given $$L (M1) subseteq L (M2)$$, M2 should also stop and be able to decide each entry.

However, option (C) also seems convincing. If for each entry, M1 says "yes" in the language, M2 should also be able to decide on this entry.

Please let me know how to approach this properly.