Please find below my solution is which is different from the exam solution:

Justification for S_{1 }with signal traces

a | (1)^{ω}

Fa | (1)^{ω}

Xa | (1)^{ω}

[Fa SB (Xa)] | (1)^{ω } {because eventually "a" holds (which is from the first point of time) before next of "a" (as next of "a" is true: self loop) and eventually "a" holds forever (self loop)}

Justification for S_{2 }with signal traces

a | (1)^{ω}

¬Xa | (0)^{ω}

(a & ¬Xa) | (0)^{ω}

F(a & ¬Xa) | (0)^{ω}

^{Please let me know if my solution is also correct or I did any mistake?}

^{In general can there be multiple solutions to these kind of questions?}

^{Thank you in advance.}