Suppose M1 and M2 are two TM’s such that L(M1) = L(M2). Then
(A) On every input on which M1 doesn’t halt, M2 doesn’t halt too.
(B) On every i/p on which M1 halts, M2 halts too.
(C) On every i/p which M1 accepts, M2 halts.
(D) None of above.
M2 accepts strings in L(M1) so definitely it will halt. Other 2 are not guaranteed as Turing machine M does not accept w if it either rejects w by halting to a reject state or loops infinitely on w.
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