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Find the Composion of this relation

  1. Sep 18, 2011 #1
    A = {1,2,3}
    B= {a,b,c}
    c = {x,y,z}

    R = {(1,a) (2,c) (3,a) (3,c)}
    S = {(b,x) (b,z) (c,y)}

    Find RoS (composition of relation)


    my solution was this:
    (2,c) belongs to R and (c,y) belongs to S so (2,y) belongs to RoS
    (3,c) belongs to R and (c,y) belongs to S so (3,y) belongs to Ros
    RoS={(2,y) 3,y}

    can we use (c,y) more than one time..
    Is this correct answer ??
     
  2. jcsd
  3. Sep 18, 2011 #2
    i think you are finding the composition relation [itex]S\circ R[/itex] since
    R is relation from A to B and S is relation from B to C. So if you are seeking
    [itex]S\circ R[/itex] , then your your first two lines are correct but the final answer
    is not since you forgot to put brackets for [itex](3,y)[/itex] .so

    [tex]S\circ R=\{(2,y),(3,y)\}[/tex]

    and its ok to use (c,y) more than one time
     
  4. Sep 18, 2011 #3

    HallsofIvy

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    Staff Emeritus
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    If you are indeed looking for RoS, then note that S "takes b into" both x and z but there is no pair in R having x or z as a first member. Similarly, S "takes c into" y but there is no pair in R having y as first member. RoS does not exist (or is the empty relation).


    To find SoR, R "takes 1 to" a but there is no pair in S with first member a so there is no pair in SoR with first member 1. R "takes 2 to" c and S "takes c to y" so SoR contains (2, y). R "take 3 to" both a and c. There is no pair in S with first member a but S "takes c to" y so (3, y) is in RoS.
     
  5. Sep 18, 2011 #4
    Thanks both of you :)
     
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