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    Determine reflexive, symmetric, antisymmetric, transitive, partial order and equivalence.

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    Let R = {(1,1)(3,1)(2,2)(1,2)(3,3)(3,2)} on Z = {1,2,3}

    Is R reflexive? Why?
    Is R Symmetric? Why?
    Is R antisymmetric? Why?
    Is R transitive? Why?
    Is R a partial order? Why?
    Is R an equivalence relation?

    © BrainMass Inc. brainmass.com December 24, 2021, 4:44 pm ad1c9bdddf
    https://brainmass.com/math/partial-differential-equations/reflexive-symmetric-antisymmetric-transitive-partial-order-4919

    Solution Preview

    1. R is reflexive since it contains (1,1),(2,2) and (3,3)
    2. R is not symmetric. It contains (3,1) but not (1,3)
    3. R is antisymmetric. We need to check that if (x,y) and (y,x) are in R then x=y. The only pairs (x,y) in R such ...

    Solution Summary

    It is determined if a relation is reflexive, symmetric, antisymmetric, transitive, partial order and its equivalence.

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