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Math Help - finite set and equivalence reltion

  1. #1
    Junior Member scottie.mcdonald's Avatar
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    finite set and equivalence reltion

    This question is confusing me, and I do not know what information is needed to solve the problem. Here is the question:

    let  \beta be the set of all finite sets. That is, elements of  \beta are finite sets. Define a relation Q on  \beta by AQB  \Leftrightarrow there is a bijection from A to B. This is an equivalence relation. Consider the quotient set  \frac{\beta}{Q} . Define a relatoin R on  \frac{\beta}{Q} by [A]R[B] if there is an injection from A to B

    a). show that R is well defined: If [A]=[A*] and [B]=[B*] then [A]R[b]  \Leftrightarrow [A*]R[B*]
    b). show that R is reflexive.
    c). show that R is transitive.
    d). show that R is antisymmetric

    what i have so far is follows:

    injective: [A]=[A*] and [B]=[B*]
     \Rightarrow [A]R[A*] and [B]R[B*] then my mind goes completely blank. i need to show injective and surjective (onto and one-one), but the orginal information i can't understand.

    Thank you,

    Scott
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  2. #2
    Junior Member scottie.mcdonald's Avatar
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    all of the letters A and B are supposed to be capitalized. I've tried editting them, but it wouldn't convert over. sorry if it's confusing.
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  3. #3
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    Are you asking about only part a)?
    If so, I fear that I can be of little help. [I confess that I don't see the point.]
    All the other parts follow from properties of bijections.
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  4. #4
    Junior Member scottie.mcdonald's Avatar
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    yes i was asking about part a). but if parts b - d are from properties of bijection, then it will take me some thinking to come up with the answer since that is not my strongest asset for proving in this class.


    any help would be appreciated,

    Thank you
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