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(B \cup C) -(B \cap C) has an even number of elements

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1986 p1

February 17, 2020
EvenSubsetscombinatorics

Problem Statement

Given n∈Nn \in N, let AA be a family of subsets of {1,2,...,n}\{1,2,...,n\}. If for every two sets B,C∈AB,C \in A the set (B∪C)−(B∩C)(B \cup C) -(B \cap C) has an even number of elements, find the largest possible number of elements of AA .
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