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  "body": "\n## Summary\n\nThe free Boolean algebra on a set $S$ is the [[Boolean algebra|0XADJKM699]] generated by $S$ with no extra relations.\nThe only equalities in it are those that hold in every Boolean algebra.\nEvery map from $S$ into a Boolean algebra extends to exactly one homomorphism from it.\nOn $n$ generators it is the algebra of all [[Boolean functions|0X05GS525E]] of $n$ variables, with $2^{2^n}$ elements.\nIt is also the Lindenbaum–Tarski algebra of classical propositional logic.\nIts propositional variables are the elements of $S$.\n\n## Explanations\n\n### L1 human\n\nTake letters $x, y, z, \\ldots$ and form all formulas with \"and\", \"or\" and \"not\".\nTwo formulas count as the same when they have the same truth table.\nThe resulting algebra is the free Boolean algebra on the letters.\nWith one letter $x$ it has four elements: false, $x$, not $x$, and true.\n",
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