which are the initial and final states?

Question

This is the exercise, I guessed I have to add $\{A,C\}$ and $\{A,B\}$ states to the table. When it comes to make the minimization, I don't know which are the final and initial states.

Image here:

Answer 1

The initial and the final states here are:

INITIAL : $S$.

FINAL : $\{A\},\{A,B\},\{A,C\}$.

And just that, cause later you 'create' states but they are different to $'\{A\}'$. They contain $\{A\}$ so they can accept.