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Math Help - Relations - Set Theory

  1. #1
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    Relations - Set Theory

    hello everyone,

    I have a problem with this question, I hope someone can help me out:

    prove that a relations R over the set A is transitive if and only if for all n>=2 R contains R^n.

    thanks !!
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  2. #2
    Super Member Rebesques's Avatar
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    contains R^n.
    ...How is this relation defined?
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  3. #3
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    Quote Originally Posted by WeeG
    hello everyone,

    R contains R^n.
    I mean that R is included in R^n

    I have no data except for that, it's a hard question....
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  4. #4
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    If R is a relation between sets A and B: that is, R \subseteq A \times B, and similarly S is a relation between B and C, then the composition R \circ S is the relation between A and C given by \{ (a,c) \in A \times C : (a,b) \in R \mbox{ and } (b,c) \in S \mbox{ for some } b \in B \}.

    If R is a relation between A and itself, then it makes sense to define R^2 as R \circ R and more generally R^n = R \circ R^{n-1}. Of course it turns out that composition is associative so that all the possible ways of defining R^n are the same.
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  5. #5
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    thanks a lot !!!!

    I am impressed !!


    thanks !
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  6. #6
    Super Member Rebesques's Avatar
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    That's the rgep we know...



    Alright Weeg, can you tackle it now?
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