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    Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity

    A)
    S = Q
    X p Y <-> ABS(X) <= ABS(Y)

    B)
    S = Z
    X p Y <-> x -y is an integral multiple of 3

    C)
    S = N
    X P Y <-> X is odd

    D)
    S = Set of all squares in the place
    S1 p S2 <-> length of side of S1 = length of side S2

    E)
    S = set of finite-length strings of characters
    X p Y <-> number of characters in x = number of characters in y

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    https://brainmass.com/math/finite-element-method/test-binary-relations-22607

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    Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity

    A)
    S = Q
    X p Y <-> ABS(X) <= ABS(Y)
    Solution. (1) Reflexivity
    Yes, since
    (2) Symmetry
    Yes, since
    (3) Antisymmetry
    No, since , but if
    (4) Transitivity
    Yes, since , we have

    B)
    S = Z
    X p Y <-> x -y is an integral multiple of 3
    Solution. (1) Reflexivity
    Yes, ...

    Solution Summary

    This shows how to test binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity

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