1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook