I am solving exam question 13.02.2019 problem 6 (d). 2019.02.13.vrs.solutions.pdf (uni-kl.de)

It asks to determinize the FG automata of part (c).

But I am confused in the solution i.e the transition for !a&!b from state P1 should go to another state Q = {{q},{p,q}}, Qf = {} because in the FG automaton in part c from the successor on input !a&!b from {q} is {{q}, {p,q}} and the successor on input !a&!b from {p,q} is {} so union is Q = {{q}, {p,q}} and for Qf the successor on input !a&!b from {p,q} is {} and the intersection with accepting state sets gives {}.

So there should be a new state like Q = {{q}, {p,q}} and Qf = {} (as drawn in my solution).

Could you please correct me what am I doing wrong or misinterpret something ?