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28 May, 08:00

Answer these questions for the poset ({2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72}, |). a) Find the maximal elements. b) Find the minimal elements. c) Is there a greatest element? d) Is there a least element? e) Find all upper bounds of {2, 9}. f) Find the least upper bound of {2, 9}, if it exists. g) Find all lower bounds of {60, 72}.

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  1. 28 May, 08:23
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    (a) maximal elements = 27,48,60,72

    (b) minimal elements = 2,9

    (c) greatest element = 2,9

    (d) least element = Does not exist

    (e) upper bounds = 18,36,72

    (f) least upper bound = 72

    (g) lower bounds = 2,4,6,12

    (h) greatest lower bound = 12
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