Results 1 to 5 of 5

Math Help - a problem with relations

  1. #1
    Newbie
    Joined
    Apr 2009
    Posts
    3

    a problem with relations

    Let M be the set of all the relation on A={1,2,3}
    Let S be the following relation on M:
    for R1, R2 relations on A, (R1,R2) S iff R1oR2 = R2oR1
    (o - composition)
    prove that S is not an equivalence relation on M

    I am having a little problem with this...
    I guess I need to prove that S is not transitive but I can't figure it out....

    any directions would be appreciated
    thanks


    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,639
    Thanks
    1592
    Awards
    1
    Let R_1  = \left\{ {(1,1),(2,2),(3,3)} \right\}\;,\,R_2  = \left\{ {(1,2),(2,3)} \right\},\;\& \,R_3  = \left\{ {(2,1),(3,2)} \right\}

    Are these true? R_1  \circ R_2  = R_2  \circ R_1 ~~\& ~~R_1  \circ R_3  = R_3  \circ R_1

    Is this true? R_3 \left( \mathcal{S} \right)R_2
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2009
    Posts
    3
    Quote Originally Posted by Plato View Post
    Let R_1  = \left\{ {(1,1),(2,2),(3,3)} \right\}\;,\,R_2  = \left\{ {(1,2),(2,3)} \right\},\;\& \,R_3  = \left\{ {(2,1),(3,2)} \right\}

    Are these true? R_1  \circ R_2  = R_2  \circ R_1 ~~\& ~~R_1  \circ R_3  = R_3  \circ R_1

    Is this true? R_3 \left( \mathcal{S} \right)R_2
    I think
    <br />
R_2  \circ R_3 = \left\{ {(2,2),(3,3)} \right\}

    <br />
R_3  \circ R_2 = \left\{ {(2,2),(1,1)} \right\} <br />
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,639
    Thanks
    1592
    Awards
    1
    Quote Originally Posted by stewie griffin View Post
    I think
    <br />
R_2  \circ R_3 = \left\{ {(2,2),(3,3)} \right\}

    <br />
R_3  \circ R_2 = \left\{ {(2,2),(1,1)} \right\} <br />
    That is correct. But both are related to R_1.
    What is wrong with that?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2009
    Posts
    3
    R_3 \left( \mathcal{S} \right)R_2  \iff  R_3  \circ R_2  = R_2  \circ R_3
    but   R_3  \circ R_2 \ne R_2  \circ R_3
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Relations and Functions - Inverse Relations Question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 13th 2011, 12:20 PM
  2. Replies: 1
    Last Post: September 19th 2011, 01:09 PM
  3. Relations problem
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 19th 2010, 07:01 AM
  4. Set Theory Relations Problem
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 15th 2010, 06:23 AM
  5. relations problem
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: August 3rd 2008, 04:50 PM

Search Tags


/mathhelpforum @mathhelpforum