Let $X$ be an arbitrary fixed set and let $\mathcal{C}$ be a nonempty class of subsets of $X$ that contains $X$. How would you prove the smallest algebra $\mathcal{C}$ consist exactly of finite intersections of finite unions of sets $A \in \mathcal{C}$ and sets $A$ such that $A^c \in \mathcal{C}$?
2026-04-13 04:22:26.1776054146
Smallest algebra generated by $\mathcal{C}$
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