{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "04T1CT7212"
    },
    {
      "field": "uses",
      "target": "05RSK4Q657"
    },
    {
      "field": "uses",
      "target": "05SZQKH75K"
    },
    {
      "field": "uses",
      "target": "09K9MWD2QQ"
    },
    {
      "field": "uses",
      "target": "09PKJKA6J0"
    },
    {
      "field": "uses",
      "target": "0DT0TCV75N"
    },
    {
      "field": "uses",
      "target": "0J0XBKG64S"
    },
    {
      "field": "uses",
      "target": "0NFAGWH84K"
    },
    {
      "field": "uses",
      "target": "0P3A06QNDP"
    },
    {
      "field": "uses",
      "target": "0RYYK8PG4S"
    }
  ],
  "body": "\n## Definition\n\nLet $p$ be a [[proposition|0ZGC7ZESYN]].\nThe negation of $p$ is the proposition $\\neg p$, read \"not $p$\".\nThe proposition $\\neg p$ is true when $p$ is false, and $\\neg p$ is false when $p$ is true.\n\n| $p$ | $\\neg p$ |\n|---|---|\n| T | F |\n| F | T |\n\n## Remarks\n\nOther notations for $\\neg p$ are $\\sim p$ and $\\overline{p}$.\nIn classical logic, $\\neg \\neg p$ has the same truth value as $p$. This is the [[double negation law|0NFAGWH84K]].\n\n## Explanations\n\n### L1 human\n\nTo negate a sentence, say that it is not the case.\nThe negation of \"$5$ is prime\" is \"$5$ is not prime\".\nThe first sentence is true, so its negation is false.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "defines": "029JBBF693",
    "kind": "definition",
    "msc": [
      "03B05"
    ],
    "name": "Negation",
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Negation"
      }
    ],
    "tag": "0XR7A7RSXB",
    "uses": [
      "0ZGC7ZESYN"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/0XR7A7RSXB/",
  "links": [
    {
      "field": "defines",
      "target": "029JBBF693"
    },
    {
      "field": "uses",
      "target": "0ZGC7ZESYN"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0XR7A7RSXB.md",
  "msc": [
    "03B05"
  ],
  "name": "Negation",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0XR/0XR7A7RSXB.md",
  "status": null,
  "tag": "0XR7A7RSXB",
  "uri": "m2://0XR7A7RSXB",
  "url": "https://math2.tamnd.com/wiki/negation-definition/",
  "writing": {
    "tag": "0XR7A7RSXB",
    "kind": "definition",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "one example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge not_instance_of in",
        "note": "one non-example that fails one clause",
        "have": 0,
        "want": 1
      }
    ]
  }
}