# Thread: VenDiagrams concerning Realtions and Equvilance classes and visualization

1. ## VenDiagrams concerning Realtions and Equvilance classes and visualization

Visualizing relations

So I am having some trouble visualizing relations. This is my analogy to
what a relation is currently.
-A relation R on A is the subset of the power set of (A X A)
Therefore the (A X A) has a R in its folder. Or R is contained in the A X A ven-diagram you know what i mean ? or is the relation an element? or is it both?
Lets give an R an arbitrary number as a relation since more than n
relations can exist
- R1 is the relation in which it sorts elements of the Cartesian product of A X A n-tuples in this
case 2-tuples, into a specific relationship
Therefore within the R1 folder exist ordered pairs which are elements of R1
Are my conclusions valid ? or are there misconceptions ?

Equivalence classes
Defining an Equivalence relations
R is an equivalence relation it is transitive reflexive and
symmetric
So let R be an equivalence relation on A
Therefore R is in A x A folder R is a subset of A x A
I don't quite understand what an Equivalence class is
my current understanding is
The Equivalence Class is in the folder of the Equivalence relation R
The Equivalence relation has to do with only either the element (a) from
the ordered pair of the relation of R or either (a) or (b)

is says in my textbook that [a]R = {s|(a,s) E R} saying that the
Equivalence class is a subset or element ?

2. okay this is what ive concluded

P(AXA) \ (AXA)\ r^*\ ordered pairs

now i need to figure out where equivalence classes go i heard they are induced by the relation, and are a subset of A ?

3. ## Equivalence Relation

Hello mikeqwerty

I don't know whether you've studied my replies in the following thread (and another one that I refer to in one of the postings), but I think you may find it helpful to do so:
http://www.mathhelpforum.com/math-he...s-classes.html