It means to take the set of things "Green object or Hat" and produce the set "Green hats". Green | Hat -> Green & Hat 2/
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Now let's decompose "Green" into "Bright Green or Dark Green" (where Dark is defined as Not Bright). Bright Green | Dark Green | Hat -> (Bright Green) & (Dark Green) & Hat No hat is both dark green and bright green at the same time. The resulting set is empty! 3/
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So depending on how you *phrase* this operation, you'll get completely different answers. Unless the union constituents are coming from a very well-defined list, it's not a particularly safe thing to do!
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Similarly, it breaks down when considering associativity: Both union and Intersection are associative, but would this theoretical operation work on the flattened result, or the original one?
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(T | U) | V -> (T | U) & V vs T | U | V -> T & U & V The two inputs are logically equivalent, but the result of this operation is completely different.
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