CTL, LTL, CTL* [2019.02 8e]

Question

I understand the solution but does my solution work too?

Answer 1

Let's check: 

• EG!a holds in states {s1;s2;s3}
• EF b holds in states {s2;s3}
• E(F b & EG!a) is equivalent to EFb & EG!a which holds in states {s2;s3}
• EF(b & EG!a) holds in states {s2;s3}

Hence, the two formulas S1 and S2 hold in exactly the same states of your structure, so that your structure does not distinguish between them.