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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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