# 2011-16 Odd Sets with Even Intersection

Let A1, A2, A3, …, An be finite sets such that |Ai| is odd for all 1≤i≤n and |Ai∩Aj| is even for all 1≤i<j≤n. Prove that it is possible to pick one element ai in each set Ai so that a1, a2, …,an are distinct.

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