Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 4J / c / i / Solution

False. Given any $D$, adjoin arbitrarily many unreachable states whose transitions remain among those new states, choosing their accepting status consistently away from the embedded copy. This produces infinitely many pairwise nonisomorphic finite deterministic automata $D^{\prime }$ containing an injective homomorphic copy of $D$.