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    S = {0, 1, 2, 4, 6}

    Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity. Also find the reflexive, symmetric and transitive closure of each relations.

    A)
    P = {(0,0), (1,1), (2,2), (4,4), (6,6), (0,1), (1,2), (2,4), (4,6) }

    B)
    P {(0,1), (1,0), (2,4), (4,2), (4,6), (6,4)}

    C)
    P ((0,0), (1,1), (2,2), 4,4), (6,6), (4,6), (6,4)}

    D)
    P = everything not equal to 0

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    https://brainmass.com/math/discrete-structures/relations-symmetric-transitive-closures-22606

    Solution Preview

    See attachment please!

    S = {0, 1, 2, 4, 6}

    Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity. Also find the reflexive, symmetric and transitive closure of each relation.

    A)
    P = {(0,0), (1,1), (2,2), (4,4), (6,6), (0,1), (1,2), (2,4), (4,6) }
    Solution: (1) Reflexivity
    Yes. Since for ,
    So, the reflexive closure of P is itself.
    (2) Symmetry
    No. Since , but
    So, the symmetric closure of P is
    P = {(0,0), (1,1), (2,2), (4,4), (6,6), (0,1),(1,0), (1,2),(2,1), (2,4), (4,2),(4,6),(6,4) }

    (3) Antisymmetry
    Yes, since it is NOT symmetric
    (4) ...

    Solution Summary

    This is a test with binary relations for reflexivity, symmetry ,antisymmetry, and transitivity; and the reflexive, symmetric and transitive closure of each relations.

    $2.49

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