{
  "aliases": [
    "addition-principle",
    "sum-rule"
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  "body": "\n## Statement\n\nLet $A$ and $B$ be finite sets with $A \\cap B = \\varnothing$.\nThen $A \\cup B$ is finite and $|A \\cup B| = |A| + |B|$.\n\nMore generally, let $A_1, \\dots, A_k$ be finite sets that are pairwise disjoint.\nThen $|A_1 \\cup \\dots \\cup A_k| = |A_1| + \\dots + |A_k|$.\n\n## Remarks\n\nFor the disjoint union $A \\sqcup B$ of two arbitrary finite sets, the same formula $|A \\sqcup B| = |A| + |B|$ holds.\nIf $A$ and $B$ are not disjoint, the formula fails. The [[inclusion-exclusion formula for two sets|0C4YEQ9H5E]] gives the correct count.\n\n## Explanations\n\n### L1 human\n\nIf you choose one item from a first group or from a second group, and no item is in both groups, you add the sizes.\nFor example, with 3 soups and 4 salads on a menu, there are $3 + 4 = 7$ ways to choose one starter.\n",
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