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Math Help - Relationship table

  1. #1
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    Relationship table

    Hi,
    I have a question that is as follows:

    "draw a talbe to show weather the following relations demostrate the following properties: symmetry, anti-symmetry, reflexivity, partial order, equivalence
    a. differs by multiple 5
    b. exaclty divides
    c. is a permutation of"

    all i can think of for
    a: reflexivity, partial order,symmetry
    b: symmetry,reflexivity
    c: anti-symmetry,equivalence

    but im not to sure im on the right path. can someone set me straight

    thanks
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  2. #2
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    Re: Relationship table

    Quote Originally Posted by nomanslan View Post
    "draw a talbe to show weather the following relations demostrate the following properties: symmetry, anti-symmetry, reflexivity, partial order, equivalence
    a. differs by multiple 5
    b. exaclty divides
    c. is a permutation of"
    There are several problems with this question.
    You failed to tell us what set these relations are defined upon.
    It appears that it may some subset of the integers.

    In any case what in the world can "permutation of" mean as a relation?
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  3. #3
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    Re: Relationship table

    it says after c. "(e.g 1,2,3,4 is a permutaion of 1,3,4,2)"

    the question doesnt give me any integers to work with. thats all there is to the question
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  4. #4
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    Re: Relationship table

    Quote Originally Posted by nomanslan View Post
    it says after c. "(e.g 1,2,3,4 is a permutaion of 1,3,4,2)" the question doesnt give me any integers to work with. thats all there is to the question
    Well then, you have not been given enough information to answer any part of the question.
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  5. #5
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    Re: Relationship table

    As Plato said, the answers to some of the questions depend on the set A on which these relations are given. I'll assume that A\subseteq\mathbb{Z}, A\ne\emptyset for (a) and (b) and A\subseteq\mathbb{Z}^n, A\ne\emptyset for some n for (c).

    Quote Originally Posted by nomanslan View Post
    "draw a talbe to show weather the following relations demostrate the following properties: symmetry, anti-symmetry, reflexivity, partial order, equivalence
    a. differs by multiple 5
    b. exaclty divides
    c. is a permutation of"

    all i can think of for
    a: reflexivity, partial order,symmetry
    If you list partial order, then you should list antisymmetry as well. In fact, antisymmetry and partial order only hold for some A. Reflexivity and symmetry are correct. This is an equivalence relation.

    Quote Originally Posted by nomanslan View Post
    b: symmetry,reflexivity
    Symmetry, antisymmetry, partial order and equivalence relation hold only for some A, reflexivity is correct.

    Quote Originally Posted by nomanslan View Post
    c: anti-symmetry,equivalence
    Antisymmetry and partial order hold for some A, symmetry, reflexivity and equivalence relation always.
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