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TR-MO-R1 2022 Problem 8

    S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\} olmak üzere, her biri çift sayıda eleman içerecek ve herhangi iki tanesinin kesişiminde çift sayıda eleman bulunacak şekilde SS nin en fazla kaç farklı alt kümesi seçilebilir? (Boş kümede çift sayıda eleman olduğu kabul ediliyor.)

    a) 16 b) 14 c) 12 d) 10 e) 8

    Official text Turkish Mathematical Olympiad, first round 2022 official paper, page 5. Quoted with source.

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