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  "body": "\n## Definition\n\nLet $U$ be a [[universal set|0BPYRMHJ48]] and let $A$ be a [[subset|0FE8Q5S42Y]] of $U$.\nThe complement of $A$ in $U$ is the set\n$$A^{c} = \\{x \\in U \\mid x \\notin A\\}.$$\n\n## Remarks\n\nOther notations are $\\overline{A}$, $A'$ and $U \\setminus A$.\nExample: in $U = \\mathbb{Z}$, the complement of the set of even integers is the set of odd integers.\nThe complement of $A^c$ is $A$, and $A \\cup A^c = U$, $A \\cap A^c = \\varnothing$.\nThe complement of $A$ in $U$ is the [[set difference|0DT0TCV75N]] $U \\setminus A$.\n\n## Explanations\n\n### L1 human\n\nThe complement is \"everything else\".\nIt depends on the universe: the complement of the even numbers is the odd numbers in $\\mathbb{Z}$, but not in $\\mathbb{R}$.\n",
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