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  "body": "\n## Statement\n\nFor all [[propositions|0ZGC7ZESYN]] $p$ and $q$, these two [[logical equivalences|06GYGS41JK]] hold.\n$$\\neg (p \\lor q) \\equiv \\neg p \\land \\neg q$$\n$$\\neg (p \\land q) \\equiv \\neg p \\lor \\neg q$$\n\n## Remarks\n\nThe first law is also valid in intuitionistic logic. In the second law, only the direction from $\\neg p \\lor \\neg q$ to $\\neg (p \\land q)$ is.\nThe laws for sets have the same form. See [[De Morgan's laws for sets|0VK0W4D5Y5]].\nThe [[negation of a universal statement|0P3A06QNDP]] is the analogue for quantifiers.\n\n## Explanations\n\n### L1 human\n\nTo negate \"and\", change it to \"or\" and negate each part.\n\"$n$ is not both even and prime\" means \"$n$ is not even, or $n$ is not prime\".\nA [[truth table|05RSK4Q657]] with four rows proves each law.\n",
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