Thanks for the clarification.

From your answer I infer the following:

So, earlier I was translating to omega automata by just looking the acceptance condition of Sing(p) and then writing equivalent representation which is given in module 6 omega automata slide 65 (Transformation of Acceptance Conditions) which is wrong.

I just need to see the given automata representation of Sing(p) or the automata drawn above for Sing(p) and just write it in symbolic representation like the states set {S}, the initial condition Q, the transition relation R, and finally the acceptance condition F.

Is this right ?

I have also updated my solution, could you please check if it is correct now ?