Problem 9a in Probability and Measure theory by Ash and Doléans-Dade reads:
Let $\mathscr C$ be an arbitrary class of subsets of $\Omega$, and let $\mathscr G$ be the collection of all finite unions $\bigcup_{i=1}^n A_i$, $n = 1, 2, \dotsc$, where each $A_i$ is a finite intersection $\bigcap_{j=1}^r B_{ij}$, with $B_{ij}$ or its complement a set in $\mathscr C$. Show that $\mathscr G$ is the minimal field (not $\sigma$-field) over $\mathscr C$.
Should I interpret $r$ as being a fixed parameter in this problem? The wording makes me think that the sets $A_i$ are actually supposed to be arbitrary finite intersections, $$ A_i = \bigcap_{j=1}^{r_i} B_{ij}, \quad r_i \in \mathbb \{0, 1, 2, \dotsc\}, $$ with $B_{ij}$ or its complement in $\mathscr C$. Maybe it will become clear while working on the problem, but I would still appreciate your input.