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  "body": "\n## Definition\n\nLet $\\varphi$ be a formula of [[propositional logic|09K9MWD2QQ]] with the propositional variables $p_1, \\dots, p_n$.\nThe formula $\\varphi$ is a tautology when $\\varphi$ is true for each of the $2^n$ assignments of truth values to $p_1, \\dots, p_n$.\n\n## Remarks\n\nExamples are $p \\lor \\neg p$ and $p \\to p$.\nA formula that is false for each assignment is a contradiction.\nA [[truth table|05RSK4Q657]] decides in a finite number of steps whether a formula is a tautology.\n\n## Explanations\n\n### L1 human\n\nA tautology is true only because of its form.\nThe sentence \"it rains or it does not rain\" is true whatever the weather.\nIts form $p \\lor \\neg p$ is a tautology.\n",
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