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Math Help - Relations of sets (again)

  1. #1
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    Relations of sets (again)

    This is my question :-


    The relation T on the set {a,b,c,d} is given by the set of pairs

    {(a,a), (b,b), (c,c), (a,c), (a,d), (b,d), (c,a), (d,a)}

    Find each of
    a)The reflexive closure of T
    b)The symetric closure of T
    c)The transitive closure of T

    Give your answers either as sets of pairs or as diagraphs



    As I said with the previous question...

    I apologize now for the fact I have not done any working out simply because I don't have a clue how to even start it! I'm trying to learn it now as I go along but don't have much time so thought I would look for help on here as well as the text book (which isn't making sense right now) so I have two points of view on the question. I'm stuck on two more questions which I will post on sperate threads too. Thanks for any help it's much appreciated.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by djmccabie View Post
    This is my question :-


    The relation T on the set {a,b,c,d} is given by the set of pairs

    {(a,a), (b,b), (c,c), (a,c), (a,d), (b,d), (c,a), (d,a)}

    Find each of
    a)The reflexive closure of T
    b)The symetric closure of T
    c)The transitive closure of T

    Give your answers either as sets of pairs or as diagraphs



    As I said with the previous question...

    I apologize now for the fact I have not done any working out simply because I don't have a clue how to even start it! I'm trying to learn it now as I go along but don't have much time so thought I would look for help on here as well as the text book (which isn't making sense right now) so I have two points of view on the question. I'm stuck on two more questions which I will post on sperate threads too. Thanks for any help it's much appreciated.
    What does the closure of a property mean?
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  3. #3
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    What does the closure of a property mean?
    I don't see where the problem refers to the closure of a property. It talks about the reflexive closure of a relation T. It is the smallest relation that contains T and is reflexive. Obviously, T\cup\{(a,a),(b,b),(c,c),(d,d)\} is the reflexive closure of T.
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  4. #4
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    Quote Originally Posted by djmccabie View Post
    This is my question :-


    The relation T on the set {a,b,c,d} is given by the set of pairs

    {(a,a), (b,b), (c,c), (a,c), (a,d), (b,d), (c,a), (d,a)}

    Find each of
    a)The reflexive closure of T
    b)The symetric closure of T
    c)The transitive closure of T

    Give your answers either as sets of pairs or as diagraphs



    As I said with the previous question...

    I apologize now for the fact I have not done any working out simply because I don't have a clue how to even start it! I'm trying to learn it now as I go along but don't have much time so thought I would look for help on here as well as the text book (which isn't making sense right now) so I have two points of view on the question. I'm stuck on two more questions which I will post on sperate threads too. Thanks for any help it's much appreciated.
    Take A = {a,b,c,d}

    Let E denote the diagonal subset of AxA.

    Let T^c denote the relation that's the converse of T.

    Let T^n denote the composition of T with itself n times.

    The reflexive closure is just T U E.

    The symmetric closure is T U T^c.

    The transitive closure is, in general, T U T^2 U ... .

    In a fixed finite case, to get it, you don't have to go out any farther than, T U T^2 U ... U T^n, where n = |A|.
    Here n=4 (pretty small), so you can just grind out its extension.
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