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Math Help - Composite of relations R and S

  1. #1
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    Composite of relations R and S

    R={(1,1),(1,4),(2,3),(3,1),(3,4)}
    S={(1,0),(2,0),(3,1),(3,2),(4,1)}

    S o R={(1,0),(1,1),(2,1),(2,2),(3,0),(3,1)}

    The book I am using is very unclear about how to construct S o R from the
    ordered pairs. I tried searching around for a quick explanation, but most of results confused me even more. If somebody could explain step by step how to get the composite of the relations R and S in this case I would really appreciate it.
    Thank you.
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  2. #2
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    R={(1,1),(1,4),(2,3),(3,1),(3,4)}
    S={(1,0),(2,0),(3,1),(3,2),(4,1)}

    S o R={(1,0),(1,1),(2,1),(2,2),(3,0),(3,1)}
    A relation is like a set of allowed steps. For example, the relation R allows stepping from 1 to 4, from 2 to 3, from 3 to 1, from 3 to 4, or remain at 1.

    For the composition S o R, one has to make two steps: first according to R, the second according to S, e.g., 2 -> 3 -> 1. Of course, the intermediate point 3 is not recorded, S o R contains just a pair (2, 1).
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  3. #3
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    e.g., 2 -> 3 -> 1

    In this example I see 1 as the final step, but how did you arrive at that?
    Does it have something to do with 1 being the second element in the pair below it?
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  4. #4
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    Quote Originally Posted by JazzGuitarist01 View Post
    R={(1,1),(1,4),(2,3),(3,1),(3,4)}
    S={(1,0),(2,0),(3,1),(3,2),(4,1)}
    S o R={(1,0),(1,1),(2,1),(2,2),(3,0),(3,1)}
    After many years of doing this, I find that if a student will just learn the definition the process will follow.
     \left( {a,b} \right) \in S \circ R if and only if there is some c such that (a,c)\in R and (c,b)\in S.

    In this case (2,1)\in S\circ R because (2,3)\in R and (3,1)\in S.

    We can take each pair in R look at the second term and see if that term is the first term in S.
    If so choose its second term.
    Example (3,{\color{blue}4})\in R and  ({\color{blue}4},1)\in S so (3,1)\in S\circ R
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