{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Definition\n\nLet $p$ and $q$ be [[propositions|0ZGC7ZESYN]].\nThe converse of the [[implication|0ZNX6DQ3EJ]] $p \\to q$ is the implication $q \\to p$.\n\n## Remarks\n\nAn implication and its converse are not [[logically equivalent|06GYGS41JK]].\nFor example, \"if $n = 2$, then $n$ is prime\" is true, but its converse \"if $n$ is prime, then $n = 2$\" is false.\nThe inverse of $p \\to q$ is $\\neg p \\to \\neg q$. It is the [[contrapositive|04T1CT7212]] of the converse.\n\n## Explanations\n\n### L1 human\n\nThe converse reads the arrow backwards.\n\"If an animal is a dog, then it is a mammal\" is true.\nIts converse, \"if an animal is a mammal, then it is a dog\", is false.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "defines": "09A3N7ZN5G",
    "kind": "definition",
    "msc": [
      "03B05"
    ],
    "name": "Converse",
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Converse_(logic)"
      }
    ],
    "tag": "0RVYE75E2M",
    "uses": [
      "0ZNX6DQ3EJ"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/0RVYE75E2M/",
  "links": [
    {
      "field": "defines",
      "target": "09A3N7ZN5G"
    },
    {
      "field": "uses",
      "target": "0ZNX6DQ3EJ"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0RVYE75E2M.md",
  "msc": [
    "03B05"
  ],
  "name": "Converse",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0RV/0RVYE75E2M.md",
  "status": null,
  "tag": "0RVYE75E2M",
  "uri": "m2://0RVYE75E2M",
  "url": "https://math2.tamnd.com/wiki/converse-definition/",
  "writing": {
    "tag": "0RVYE75E2M",
    "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
      }
    ]
  }
}