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  "body": "\n## Definition\n\nLet $A$ and $B$ be [[sets|0SJ3RX9TXA]].\nThe intersection of $A$ and $B$ is the set\n$$A \\cap B = \\{x \\in A \\mid x \\in B\\}.$$\nSo an object $x$ is an [[element|0EZ758XE73]] of $A \\cap B$ when $x \\in A$ and $x \\in B$.\n\n## Remarks\n\nExample: $\\{1, 2\\} \\cap \\{2, 3\\} = \\{2\\}$.\nIntersection is commutative and associative, and $A \\cap B \\subseteq A$.\nWhen $A \\cap B = \\varnothing$, the sets are [[disjoint|0W4RPA8QH3]].\nThe intersection of a family of sets is in [[intersection of a family of sets|0839XNQXDK]].\n\n## Explanations\n\n### L1 human\n\nThe intersection keeps only what the two sets have in common.\nThe intersection of the even numbers and the multiples of $3$ is the set of multiples of $6$.\n",
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