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Even Subsets

A set \(T\) is called even if it has even number of elements. Let \(n\) be a positive even integer, and let \(S_1, S_2, \dots, S_n\) be even subsets of the set \(S = \){\(1,2,\dots,n\)}.

  • Prove that there exist \(i\) and \(j\), \(1 \leq i < j \leq n\), such that \(S_i \cap S_j\) is even.
Source: from book "102 Combinatorial Problems"

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