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  "body": "\n## Statement\n\nLet $A$ and $B$ be finite sets.\nThen\n$$|A \\cup B| + |A \\cap B| = |A| + |B|.$$\nEquivalently, $|A \\cup B| = |A| + |B| - |A \\cap B|$.\n\n## Remarks\n\nIf $A \\cap B = \\varnothing$, this is the [[rule of sum|0EE2V3CHFK]].\nFor three sets: $|A \\cup B \\cup C| = |A| + |B| + |C| - |A \\cap B| - |A \\cap C| - |B \\cap C| + |A \\cap B \\cap C|$.\nThe [[inclusion–exclusion principle|0FF7726C7P]] is the version for $n$ sets.\n\n## Explanations\n\n### L1 human\n\nWhen you add the sizes of $A$ and $B$, you count the elements of both sets twice.\nSubtract the size of $A \\cap B$ once to correct this. For example, $12$ students play football, $8$ play chess, and $3$ do both, so $17$ students do at least one.\n",
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