Item 8 (0011) — 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 Over Unions. Let $X$ be a set. For each $U,V,W\in \mathcal{P}\webleft (X\webright )$, we have equalities
\begin{align*} U\times \webleft (V\cup W\webright ) & = \webleft (U\times V\webright )\cup \webleft (U\times W\webright ),\\ \webleft (U\cup V\webright )\times W & = \webleft (U\times W\webright )\cup \webleft (V\times W\webright ) \end{align*}

of subsets of $\mathcal{P}\webleft (X\times X\webright )$.

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