{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nA vacuous truth is an [[implication|0ZNX6DQ3EJ]] or a universal statement that is true because its hypothesis is never true.\nAn implication $p \\to q$ with a false $p$ is true, and a statement $\\forall x \\in X, \\, P(x)$ with an empty $X$ is true.\n\n## Remarks\n\nExample: \"each element of the [[empty set|0ECVK59Y03]] is an even number\" is vacuously true.\nVacuous truth explains why the empty set is a [[subset|0FE8Q5S42Y]] of every set.\n\n## Explanations\n\n### L1 human\n\n\"All unicorns in this room are blue\" is true when the room has no unicorns.\nThere is nothing that can break the statement.\nThis convention keeps the rules of logic simple and regular.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "kind": "concept",
    "msc": [
      "03B05"
    ],
    "name": "Vacuous truth",
    "same_as": {
      "wikidata": "Q1096079",
      "wikipedia": "Vacuous truth"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Vacuous_truth"
      }
    ],
    "tag": "0V4QXPGJQK",
    "uses": [
      "0ZNX6DQ3EJ",
      "0B88PQTJ66"
    ]
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0V4QXPGJQK/",
  "links": [
    {
      "field": "uses",
      "target": "0ZNX6DQ3EJ"
    },
    {
      "field": "uses",
      "target": "0B88PQTJ66"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0V4QXPGJQK.md",
  "msc": [
    "03B05"
  ],
  "name": "Vacuous truth",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0V4/0V4QXPGJQK.md",
  "status": null,
  "tag": "0V4QXPGJQK",
  "uri": "m2://0V4QXPGJQK",
  "url": "https://math2.tamnd.com/wiki/vacuous-truth/",
  "writing": {
    "tag": "0V4QXPGJQK",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}