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Math Help - Equivalence classes

  1. #1
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    Equivalence classes

    Hello there,

    I have troubles with finding equivalence classes for my homework.
    Question goes like this:
    Let A={1,2,3,4} and B = {2,4}. P(A) is power set. Relation R defined on P(A) by
    X R Y, X, Y elements of P(A) if X ∩ B = Y ∩ B. Now, i have to show that R is equivalence relation on P(A), which i did. and i have to find equivalence classes for R.
    Now, im stuck here.. im not too sure how start it. I was wondering if you could guide me please.

    Thank you in advance.

    EDIT: SOLVED>
    Last edited by Lowoctave; November 13th 2011 at 01:28 PM. Reason: Problem Solved
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Equivalence classes

    Perhaps the following outline can help you. Given X\in P(A) we have four cases:

    (i)\;X\cap B=\emptyset\quad (ii)\;X\cap B=\{2\}\quad (iii)\;X\cap B=\{4\}\quad (iv)\;X\cap B=B\quad

    So , [\;\emptyset\;]=\{\;\emptyset,\{1\},\{3\},\{1,3\}\;\} , etc
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  3. #3
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    Re: Equivalence classes

    I have only one question sir,

    how did you find [∅] = {∅, {1}, {3}. {1,3}}? I have troubles understanding that..
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Re: Equivalence classes

    Quote Originally Posted by Lowoctave View Post
    how did you find [∅] = {∅, {1}, {3}. {1,3}}? I have troubles understanding that..
    We have found all elements Y\in P(A) such that \emptyset\cap B=Y\cap B that is , all elements Y\in P(A) such that \emptyset\; R\; Y .
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  5. #5
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    Re: Equivalence classes

    Alrighty! makes sense! thank you very much sir
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