How can I proof that all $\mu^*$ measurable set is a $\sigma$ algebra

Question

Hi according to wiki a $\mu^*$ measurable set satisfy $\forall A\subset X\rightarrow\mu^*(A)=\mu^*(A\cap S)+\mu^*(A\setminus S)$

I would like to prove that all set that is $\mu^*$ measurable is a $\sigma$ algebra of $X$

More specifically, I would like to prove if $S_1,S_2$ is $\mu^*$ measurable sets of $X$ then $\forall A\subset X\rightarrow\mu^*(A)=\mu^*(A\cap (S_1\cup S_2))+\mu^*(A/(S_1\cup S_2))$

Can anyone help me on that..... Thanks a lot