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  "body": "\n## Example\n\nLet $X$ be a set, and let $\\mathcal{P}(X)$ be the set of all subsets of $X$.\nWith $A \\wedge B = A \\cap B$, $A \\vee B = A \\cup B$, $\\neg A = X \\setminus A$, $0 = \\varnothing$ and $1 = X$, the set $\\mathcal{P}(X)$ is a [[Boolean algebra|06GKBTAA5E]].\nIts order is inclusion $\\subseteq$.\n\n## Remarks\n\nIf $X$ has $n$ elements, this Boolean algebra has $2^n$ elements.\nA field of sets on $X$ is a subset of $\\mathcal{P}(X)$ that contains $\\varnothing$ and is closed under complement and binary union. It is a Boolean subalgebra.\nEvery finite Boolean algebra is isomorphic to a power set Boolean algebra, by [[Stone's representation theorem for finite Boolean algebras|0DYS9C3HH5]].\n\n## Explanations\n\n### L1 human\n\nThe subsets of a set form a Boolean algebra: intersection is and, union is or, and complement is not.\nVenn diagrams show the laws of this Boolean algebra.\n",
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