Answer

Correct Option: (i) The set of states reachable using $\epsilon$ only

Explanation

$\epsilon$-closure $\text{ECLOSE}(q)$ for NFA-$\epsilon$:

$\text{ECLOSE}(q) = \{ p \mid q \xrightarrow{\epsilon^*} p \}$ — all states reachable from $q$ by zero or more $\epsilon$-moves, including $q$ itself.

Example: $q_0 \xrightarrow{\epsilon} q_1 \xrightarrow{\epsilon} q_2$ → ECLOSE($q_0$) = $\{q_0,q_1,q_2\}$.

Used in subset construction for $\epsilon$-NFA → DFA/NFA conversion: $\delta_D(S,a) = \text{ECLOSE}(\bigcup_{q\in S} \delta(q,a))$.

Other options are incorrect: not unreachable, not just finals, not dead states.

Final Answer

$\epsilon$-closure = states via $\epsilon$ only → Option (i).