# Sigma algebra generated by $I_{d}$

Question is to show that $$S(I_{d})=B_{R} \cap [0,1]$$, where $$I_{d}$$ denote the class of all subintervals of $$[0,1]$$ with dyadic endpoints and $$B_{R}$$ is sigma algebra of borel subsets of $$R$$. I have no idea to proceed with this. Any hint please.

If $$U$$ is open and $$x \in U$$ then there is a dyadic interval $$I_d$$ such that $$x \in I_d \subset U$$. From this conclude that $$U$$ is a (countable) union of dyadic intervals. Can you complete the argument now?.