$$ M1 = < \{A,B,C\}, \{a\}, \{(A, a)\} \to B, (A, a) \to C\}, A, \{B\} >$$
Assume that $T(M1) = {a}$. Use proven constructions to derive a DFSA, $M2$, from $M1$ such that $T(M2) = T(M1)$.
My thought about it is it will be the following: $$ M2 = < \{A,B\}, \{a\}, \{(A, a)\} \to B\}, A, \{B\} > $$
i.e. C isn't included since it is not a final state, it will be a state which if is reached the system would crash. Is my reasoning correct?