Understanding Set Theory: Equivalence Relations and Partitions Explained

[ElDavidas]

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 $$f: A \rightarrow B$$be a function. For each b $$\epsilon$$ 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.

 

[Hurkyl]

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

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

For each b $$\epsilon$$ ran f.

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 $\in$ (which is preferable to $\epsilon$) here is no better than simply saying the word "in" -- IMHO using the word would have been more readable.

Show that the collection of all subsets Ab of A is a partition of A

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