Results 1 to 4 of 4

Math Help - Bijective Equivalence relation proof

  1. #1
    Newbie
    Joined
    Dec 2009
    Posts
    2

    Bijective Equivalence relation proof

    Let U be a family of all finite sets. Define the relation ~1 on U as follows

    A1 ~1 A2 iff there is a bijection f: A1->A2

    Prove that ~1 is an equivalence relation and describe the equivalence classes.

    I can't seem to remember how to do this. I forgot this part of Set Theory. Thank you to anyone for help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Quote Originally Posted by selkam47 View Post
    Let U be a family of all finite sets. Define the relation ~1 on U as follows
    A1 ~1 A2 iff there is a bijection f: A1->A2
    Prove that ~1 is an equivalence relation and describe the equivalence classes. I can't seem to remember how to do this. I forgot this part of Set Theory.
    Have you looked it up?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2009
    Posts
    2
    I did look it up, I'm just having trouble doing it for an undefined bijection
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member qspeechc's Avatar
    Joined
    Oct 2007
    Posts
    73
    Ok, is the relation reflexive? That is, can you find a bijection from a set to itself? Of course you can! The trivial bijection of mapping each element to itself.

    Is the relation symmetric? Say you are given a bijection from A1 to A2, is there a bijection from A2 to A1? Yes. A bijection is invertible, and its inverse is also a bijection.

    Is the relation transitive? If there is a bijection from A1 to A2, and a bijection from A2 to A3, is there a bijection from A1 to A3? There is indeed, and what function gives this bijection?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. equivalence relation proof
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 3rd 2011, 05:18 AM
  2. Equivalence relation proof
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: May 17th 2011, 04:30 PM
  3. Equivalence Relation Proof
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: March 25th 2011, 08:32 AM
  4. Equivalence Relation Proof
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: August 5th 2009, 12:19 PM
  5. equivalence relation proof
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: July 3rd 2006, 01:46 PM

Search Tags


/mathhelpforum @mathhelpforum