{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "07C4A8Y18K"
    }
  ],
  "body": "\n## Definition\n\nA literal is a propositional variable $p$ or its negation $\\neg p$.\nA formula of propositional logic is in disjunctive normal form if it is a disjunction of one or more conjunctions of one or more literals.\n\n## Remarks\n\nExample: $(p \\wedge \\neg q) \\vee (q \\wedge r) \\vee \\neg p$ is in disjunctive normal form.\nEvery formula is logically equivalent to a formula in disjunctive normal form. For a formula that is not a contradiction, take one conjunction for each row of the truth table where it is true.\nA consequence: the connectives $\\wedge$, $\\vee$ and $\\neg$ are functionally complete.\n\n## Explanations\n\n### L1 human\n\nA formula in disjunctive normal form is an or of ands of simple conditions.\nIt lists all the cases in which the formula is true.\n",
  "commit": "545acf83a9b75c8ddc375ef8b23d2ae101a4d7e4",
  "front": {
    "defines": "0GVDFAY4KW",
    "kind": "definition",
    "msc": [
      "03B05"
    ],
    "name": "Disjunctive normal form",
    "sources": [
      {
        "locator": "Definition",
        "url": "https://en.wikipedia.org/wiki/Disjunctive_normal_form"
      }
    ],
    "tag": "06S4WGSEQA"
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/06S4WGSEQA/",
  "links": [
    {
      "field": "defines",
      "target": "0GVDFAY4KW"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/06S4WGSEQA.md",
  "msc": [
    "03B05"
  ],
  "name": "Disjunctive normal form",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/06S/06S4WGSEQA.md",
  "status": null,
  "tag": "06S4WGSEQA",
  "uri": "m2://06S4WGSEQA",
  "url": "https://math2.tamnd.com/wiki/disjunctive-normal-form-definition/",
  "writing": {
    "tag": "06S4WGSEQA",
    "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
      }
    ]
  }
}