Item 7 (01HF) — The Clowder Project

Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

Distributivity of Unions Over Intersections. The diagrams
commute, i.e. we have equalities of sets
\begin{align*} U\cup \webleft (V\cap W\webright ) & = \webleft (U\cup V\webright )\cap \webleft (U\cup W\webright ),\\ \webleft (U\cap V\webright )\cup W & = \webleft (U\cup W\webright )\cap \webleft (V\cup W\webright ) \end{align*}

for each $U,V,W\in \mathcal{P}\webleft (X\webright )$.

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