Item 17 (005Q) — 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`

Interaction With Powersets and Groups. Let $X$ be a set.
1. The quadruple $\webleft (\mathcal{P}\webleft (X\webright ),\mathbin {\triangle },\text{Ø},\text{id}_{\mathcal{P}\webleft (X\webright )}\webright )$ is an abelian group.¹
2. Every element of $\mathcal{P}\webleft (X\webright )$ has order $2$ with respect to $\mathbin {\triangle }$, and thus $\mathcal{P}\webleft (X\webright )$ is a Boolean group (i.e. an abelian $2$-group).

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