Results 1 to 4 of 4

Math Help - VenDiagrams concerning Realtions and Equvilance classes and visualization

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    8

    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 ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2009
    Posts
    8
    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 ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    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

    Grandad
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2009
    Posts
    8
    hey grandad yeha ive read it i know what an equivalence relation its s standard relation so it would fit in this type of organization

    P(AXB)
    => (AXB) (A2XB2) ...
    =>(aRb eq) (aRb eq2) ...
    =>abstract formula for relation or ordered pair
    some one told me that equivalence classes are on a single letter of the ordered pair which say the equivalence class of a from the ordered pair, which is induced by the relation, and are a subset of A or belongs to A. can you clarify where a a equivalence class would go ?
    => means in the folder or super set
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. r formula visualization
    Posted in the Trigonometry Forum
    Replies: 18
    Last Post: November 20th 2010, 04:37 AM
  2. conjugacy classes
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 16th 2009, 11:25 AM
  3. classes
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: October 8th 2009, 04:28 PM
  4. 3-d visualization problem
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 17th 2009, 04:49 AM
  5. Tensor Visualization
    Posted in the LaTeX Help Forum
    Replies: 10
    Last Post: September 22nd 2007, 07:29 PM

Search Tags


/mathhelpforum @mathhelpforum