Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Relations (Relation inside a Relation)

  1. Dec 7, 2015 #1
    I have a question about what I would call a relation inside a relation. Like:

    A={1,2,3) and B={a,b,c}

    R1={(a,1) ,(a,3), (b,2), (c,1,), (c,3) }

    R2={(a,a), (b,a), (b,c), (c,a) }

    R3=R1R2

    Like this. I have 2 regular relations. Then I form another relation using these 2. How do I do that? Like if you want to map it or show their common sets.
    I would say there's none.
     
  2. jcsd
  3. Dec 7, 2015 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    You have to define what "R1R2" is supposed to mean. The answer will be completely dependent on that definition.
     
  4. Dec 7, 2015 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Do you mean ##R_1\circ R_2##?
     
  5. Dec 23, 2015 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    It looks like you mean the "composition", the ##R_1 \circ R_2## that micromass suggested. If so then it would be given by;
    Since ##R_2## contains (a, a) while ##R_1## contains (a, 1) and (a, 3), ##R_3## contains both (a, 1) and (a, 3). Since ##R_2## contains (b, a) while ##R_1## contains (a, 1) and (a, 3), ##R_3## contains (b, 1) and (b, 3). Since ##R_2## contains (b, c) while ##R_1## contains (c, 1) and (c, 3), ##R_2## contains (b,1) and (b, 3)- but we already have those. Since ##R_2## contains (c, a) while ##R_1## contains (a, 1) (a, 3) ##R_3## contains (c, 1) and (c, 3).

    ##R_3##= {(a, 1), (a, 3), (b, 1), (b, 3), (c, 1), (c, 3)}.
     
    Last edited by a moderator: Dec 23, 2015
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Relations (Relation inside a Relation)
  1. Empty relation (Replies: 3)

  2. Equivalence Relations (Replies: 4)

  3. Relations and sets (Replies: 3)

Loading...