Answer

Correct Option: (i) $m \le 2^{n}$

Explanation

Same as Q28 / Q87: Subset construction.

NFA $n$ states → DFA has at most $2^{n}$ subsets. Minimized DFA $m$ ≤ subset DFA ≤ $2^{n}$.

• (ii) $n \le m$ is not necessarily true (NFA can be smaller).
• (iv) $m =2^{n}$ is not always (upper bound, but often smaller).
• (iii) one accept state is false (can be multiple).

Final Answer

$m \le 2^{n}$ → Option (i).