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  "body": "\n## Proof\n\nWe compute the [[truth table|05RSK4Q657]] of $p \\lor \\neg p$.\n\n1. Let $p$ be a [[proposition|0ZGC7ZESYN]]. In classical logic, $p$ has exactly one of the two truth values, true or false.\n2. Suppose $p$ is true. By the definition of [[disjunction|0H5GKDTB01]], $p \\lor \\neg p$ is true, since its first part is true.\n3. Suppose $p$ is false. By the definition of [[negation|0XR7A7RSXB]], $\\neg p$ is true.\n4. In the case of step 3, $p \\lor \\neg p$ is true by the definition of disjunction, since its second part is true.\n5. The two rows of the truth table are these.\n\n| $p$ | $\\neg p$ | $p \\lor \\neg p$ |\n|---|---|---|\n| T | F | T |\n| F | T | T |\n\n6. By step 1, steps 2 and 4 cover every possible truth value of $p$. In each case $p \\lor \\neg p$ is true. So $p \\lor \\neg p$ is true for each proposition $p$.\n\n## Idea\n\nIn classical logic a proposition has only two possible truth values. If $p$ is true, the first part of $p \\lor \\neg p$ is true. If $p$ is false, the second part is true. Either way the disjunction is true.\n",
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