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Set Theory 2 Questions

  1. Jan 8, 2006 #1
    Does anybody in here know their Set Theory really well? I could do with some help on a few questions!!

    Q1) Show how an equilance relation on a set X leads to a partition of X?

    Q2) Let A and B be sets and [tex] f: A \rightarrow B [/tex]be a function. For each b [tex]\epsilon[/tex] ran f. Show that the collection of all subsets Ab of A is a partition of A and show how this partition can arise as a collection of equivalence classes under an equilavence relation on A determined by f.

    I keep on reading my notes, but I don't quite understand how the terms equivalence relation, partition and equivalence classes all coincide with one another.
     
    Last edited: Jan 8, 2006
  2. jcsd
  3. Jan 8, 2006 #2

    Hurkyl

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    Well, start simple: what is an equivalence relation on X? What is a partition on X?

    This was confusing at first -- it didn't help that my browser decided to put a line break between "ran" and "f". The first tip is when putting symbols in paragraphs, use [ itex ] instead of [ tex ]. Secondly, using the symbol [itex]\in[/itex] (which is preferable to [itex]\epsilon[/itex]) here is no better than simply saying the word "in" -- IMHO using the word would have been more readable.

    You've not defined the term "Ab" anywhere in your post... (Yes, I know you meant something like [itex]A_b[/itex], but you've not said what that means)
     
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