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The Inclusion-Exclusion formula expresses the size of a union of a family of sets in terms of the sizes of intersections of all subfamilies. This paper considers approximating the size of the union when intersection sizes are known for only some of the subfamilies, or when these quantities are given to within some error, or both. In particular, we consider the case when all k-wise intersections are given for every k K: It turns out that the answer changes in a signi cant way around K = p n : ifdoi:10.1007/bf02128670 fatcat:n7dt3hdd3rf37gtl7mgkrsn7ba