Suppose that $A$ is some class of subsets of the space $\Omega$, and let $f(A)$ denote the field generated by $A$. I am attempting to prove the following:
If the set $B$ belongs to $f(A)$, then B can be expressed as $B=\cup_{i=1}^m\cap_{j=1}^{n_i}A_{i_j}$, where the $m$ sets $\cap_{j=1}^{n_i}A_{i_j}$ are disjoint, and either $A_{i_j}$ belongs to $A$ or $A_{i_j}^c$ belongs to $A$.
I've been stuck on this question for a while now, so I'd like to see a proof or get some sort of hint.