A regular language $L$ is accepted by a non-deterministic finite automaton (NFA) with $n$ states. Which of the following statement(s) is/are FALSE?

Let an NFA $N$ have $n$ states accepting language $L$.

1. Option (A): *"$L$ may have an accepting NFA with $< n$ states."*

   • This is TRUE. If the given $n$-state NFA contains redundant or unreachable states, there may exist an equivalent NFA with fewer states.

2. Option (B): *"$L$ may have an accepting DFA with $< n$ states."*

   • This is TRUE. An NFA with non-minimal states can be equivalent to a minimal DFA having strictly fewer than $n$ states (e.g., an NFA with redundant states accepting $\Sigma^*$).

3. Option (C): *"There exists a DFA with $\le 2^n$ states that accepts $L$."*

   • This is TRUE. By the subset (powerset) construction, every NFA with $n$ states can be converted into an equivalent DFA with at most $2^n$ states.

4. Option (D): *"Every DFA that accepts $L$ has $> 2^n$ states."*

   • This is FALSE. Since the subset construction always yields an equivalent DFA with at most $2^n$ states, it is impossible for all equivalent DFAs to require more than $2^n$ states.

Since the question asks for the statement(s) that is/are FALSE, the correct option is (D).