Results 1 to 2 of 2

Math Help - Equivalence of two sets

  1. #1
    jfk
    jfk is offline
    Newbie jfk's Avatar
    Joined
    Mar 2012
    From
    ...
    Posts
    23

    Equivalence of two sets

    Please I need help proving the following question:
    Given an infinite set A and a countable set B, prove that {A}\cup{B}\sim{A}.
    I already proved the case when {A}\cap{B}=\emptyset and when {B}\subset{A}.
    I need help proving what happens when {B}\nsubseteq{A} and {A}\cap{B}\neq\emptyset
    10x in advance...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,535
    Thanks
    778

    Re: Equivalence of two sets

    Well, B=B_1\cup B_2 for some B_1, B_2 such that B_1\subseteq A and B_2\cap A=\emptyset. The sets B_1 and B_2 are countable. Therefore, A\cup B=A\cup B_1\cup B_2=A\cup B_2\sim A by what you have already proved.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: January 14th 2010, 12:28 PM
  2. equivalence relation and equivalence classes
    Posted in the Discrete Math Forum
    Replies: 6
    Last Post: January 7th 2010, 06:36 PM
  3. Equivalence relation and order of each equivalence class
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 30th 2009, 09:03 AM
  4. Sets, Equivalence Class/Relations
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 22nd 2009, 01:54 PM
  5. Equivalence relation and Equivalence classes?
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: January 7th 2009, 03:39 AM

Search Tags


/mathhelpforum @mathhelpforum