Hello,

the problem is the following: Let $\displaystyle A, B \subseteq \Omega$. Find the smallest $\displaystyle \sigma$-algebra ($\displaystyle \mathcal{F}$) on $\displaystyle \Omega$ containing the sets $\displaystyle A$ and $\displaystyle B$.

I have tried to answer this, and would appreciate if you could tell me if this the correct answer, or if I have left something out:

$\displaystyle \{

\emptyset, \Omega, A, B, A^c, B^c, A \cup B, A \cap B, A \Delta B , A \backslash B, B \backslash A,$$\displaystyle

(A \cup B)^c, (A \cap B)^c, (A \Delta B)^c , (A \backslash B)^c, (B \backslash A)^c \}$

Thanks!