{
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  "body": "\n## Statement\n\nLet $A$, $B$ and $C$ be [[sets|0SJ3RX9TXA]].\nThen intersection distributes over union, and union distributes over intersection:\n$$A \\cap (B \\cup C) = (A \\cap B) \\cup (A \\cap C),$$\n$$A \\cup (B \\cap C) = (A \\cup B) \\cap (A \\cup C).$$\n\n## Remarks\n\nThe laws follow from the distributive laws of logic for $\\land$ and $\\lor$.\nThe second law has no analogue for numbers: $a + bc$ is not $(a + b)(a + c)$ in general.\n\n## Explanations\n\n### L1 human\n\nTo prove the first law, take $x$ in the left side. Then $x \\in A$, and $x \\in B$ or $x \\in C$.\nIn the first case $x \\in A \\cap B$, and in the second case $x \\in A \\cap C$.\nThe other inclusion is similar.\n",
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