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  "body": "\n## Statement\n\nEach of the identities stated above is one of a pair of identities such that each can be transformed into the other by interchanging $\\cup$ and $\\cap$, while also interchanging $\\varnothing$ and $\\boldsymbol{U}$.\n\nThese are examples of an extremely important and powerful property of set algebra, namely, the **principle of duality** for sets, which asserts that for any true statement about sets, the **dual** statement obtained by interchanging unions and intersections, interchanging $\\boldsymbol{U}$ and $\\varnothing$ and reversing inclusions is also true. A statement is said to be **self-dual** if it is equal to its own dual.\n",
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