How to find sigma-algebra over omega3 generated by the log-return ln(S2/S1) and ln(S3/S2)?

Question

I calculated {S2/S1} = {u, u*u/d, d, d*d/u}, and then get ln(S2/S1)= {ln(u),ln(u*u/d), ln(d),ln( d*d/u)}. I am not sure my way of doing this question is right, because i m confuse about how to get its sigma-algebra.

Could someone tell me whether this way is right or not?