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Math Help - How to proof this?

  1. #1
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    Question How to proof this?

    Hi there! I've got a question.

    You have got:
    X and Y are non empty sets.
    You know that the set {Ai} for i in Y is a family of equivalence relations on X, indexed by Y.

    How can you show that the set {q | q in Ai for all i in Y} is an equivlance relation on X?

    Bye!
    Mary
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  2. #2
    MHF Contributor

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    Quote Originally Posted by MaryB View Post
    X and Y are non empty sets.
    You know that the set {Ai} for i in Y is a family of equivalence relations on X, indexed by Y. How can you show that the set {q | q in Ai for all i in Y} is an equivlance relation on X?
    There seems to be something wrong with the way you have written the question.
    Any relation is set of ordered pairs.
    The given set is a set of sets of ordered pairs. I am not sure what to make of that?
    Morever, in order to have an equivalence relation we need a relationship between the members of each pair.

    Perhaps you could post the question exactly as it appears in you assignment.
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  3. #3
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    Sorry, here is the whole assignment:
    Let X and Y be non empty sets.
    Let {Ai} i in Y be a family of equivalence relations on X, indexed by Y.
    Show that {q | q in Ai for all i in Y} is an equivalence relation on X.

    That's it
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  4. #4
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    Never you mind, there is a piece missing!

    My teacher copied it for me, but she did it wrong so there is some information missing.
    Can I delete a question?
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