{
  "aliases": [
    "contraposition",
    "law-of-contraposition"
  ],
  "backlinks": [
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  "body": "\n## Statement\n\nLet $p$ and $q$ be [[propositions|0ZGC7ZESYN]].\nThe [[implication|0ZNX6DQ3EJ]] $p \\to q$ is [[logically equivalent|06GYGS41JK]] to its contrapositive $\\neg q \\to \\neg p$.\n$$p \\to q \\equiv \\neg q \\to \\neg p$$\n\n## Remarks\n\nThe direction from $p \\to q$ to $\\neg q \\to \\neg p$ is valid in intuitionistic logic. The other direction needs classical logic.\nThis equivalence is the basis of [[proof by contrapositive|0BB5TPGQ1N]].\nDo not confuse the contrapositive with the [[converse|0RVYE75E2M]] $q \\to p$.\n\n## Explanations\n\n### L1 human\n\n\"If it rains, the street is wet\" says the same as \"if the street is not wet, it does not rain\".\nBoth sentences are false in exactly one case: rain and a dry street.\n",
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    "aliases": [
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    "name": "Contrapositive",
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  "markdown": "https://math2.tamnd.com/node/04T1CT7212.md",
  "msc": [
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  "name": "Contrapositive",
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  "role": "theorem",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/04T/04T1CT7212.md",
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  "tag": "04T1CT7212",
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  "url": "https://math2.tamnd.com/wiki/contrapositive/",
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    "tag": "04T1CT7212",
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