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  "body": "\n## Statement\n\nLet $U$ be a finite set and let $A \\subseteq U$.\nLet $A^c = U \\setminus A$ be the complement of $A$ in $U$.\nThen $|A^c| = |U| - |A|$.\n\n## Remarks\n\nThe rule follows from the [[rule of sum|0EE2V3CHFK]], because $U$ is the disjoint union of $A$ and $A^c$.\nIt is useful when the complement is easier to count. For example, the number of words of length $n$ over $\\{0, 1\\}$ that contain at least one $1$ is $2^n - 1$.\n\n## Explanations\n\n### L1 human\n\nSometimes it is easier to count what you do not want.\nTo count the outcomes with at least one six in two dice rolls, count the outcomes with no six: $5 \\cdot 5 = 25$. Then $36 - 25 = 11$ outcomes have at least one six.\n",
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