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Math Help - Equivalence Relations and Partial Orderings

  1. #1
    anu
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    Equivalence Relations and Partial Orderings

    1. Give an interpretation of the equivalence classes for the equivalence relation R in: Let R be the relation on the set of ordered pairs of positive integers such that ((a,b),(c,d)) ℇ R if and only if ad = bc.

    2) suppose that R1 and R2 are equivalence relations on the set S. Determine whether each of these combinations of R1 and R2 must be an equivalence relation.
    a) R1 U R2
    b) R1 ∩ R2
    c) R1 ⊕ R2

    3) Do we necessarily get an equivalence relation when we form the symmetric closure of the reflexive closure of the transitive closure of a relation?

    4) Give an example of an infinite lattice with both a least and a greatest element.

    Thank You
    Last edited by anu; October 31st 2007 at 11:00 PM. Reason: errors
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  2. #2
    anu
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    6) Answer these questions for the poset ({2, 4, 6, 9, 12, 18, 27, 36, 48, 60, 72}, |}. Are the answers correct?

    (a) Find the maximal elements.
    27, 48, 60, 72

    (b) Find the minimal elements.
    2, 9

    (c) Is there a greatest element?
    No.

    (d) Is there a least element?
    No.

    (e) Find all upper bounds of {2, 9}.
    18, 36, 72

    (f) Find the least upper bound of {2, 9}, if it exists.
    18

    (g) Find all lower bounds of {60, 72}.
    2,4,6,12

    (h) Find the greatest lower bound of {60, 72}, if it exists.
    12

    Can some teach me how to draw Hasse diagram! ---Got it!!! yeah

    Last edited by anu; October 31st 2007 at 11:00 PM.
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