VRS - LTL to Deterministic safety automata

Question

Problem 7b

In the solution provided, it is mentioned that the state transition diagram is not needed.
How does one do subset construction without making the state transition diagram?

Answer 1

Good point, the remark does not make sense. The thought was that only the reachable states will be needed, but all the states of that automaton are reachable, so that the entire state transition diagram is in fact needed.