n-ary Symmetric Difference
As above, the symmetric difference of a collection of sets contains just elements which are in an odd number of the sets in the collection:
- .
Evidently, this is well-defined only when each element of the union is contributed by a finite number of elements of .
Suppose is a multiset and . Then there is a formula for, the number of elements in, given solely in terms of intersections of elements of :
- ,
where is meant to indicate that is a subset of distinct elements of, of which there are .
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