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Math Help - [SOLVED] Composition of relations. Finding R^3

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    Thumbs up [SOLVED] Composition of relations. Finding R^3

    If A={1,2,3,4} and Relations R={(1,1),(1,2),(2,3),(3,4)} Find R^3?

    Here R^3 means R o R o R.

    First We calculate R o R. And Then we have to take the composition of RoR and R.

    My question Whether we have to compute (RoR) o R or (RoR) o R , because both gives a different result.

    The convention used here is, The composition of R and S is S o R.

    R o R = { (1,2),(1,3),(2,4)}
    (RoR) o R = {(1,2),(1,3),(1,4)}
    and R o (R o R) = {(1,3),(1,4)}


    so Which R^3 among the above 2 is correct?
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  2. #2
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    Quote Originally Posted by sudeepmansh View Post
    If A={1,2,3,4} and Relations R={(1,1),(1,2),(2,3),(3,4)} Find R^3?
    My question Whether we have to compute (RoR) o R or (RoR) o R , because both gives a different result.
    R o R = { (1,2),(1,3),(2,4)}
    (RoR) o R = {(1,2),(1,3),(1,4)}
    and R o (R o R) = {(1,3),(1,4)}
    In fact they are not different.
    You missed this: R\circ R=\{{\color{blue}(1,1)},(1,2),(1,3),(2,4)\}<br />

    It is a theorem: If each of R,~S,~\&~T is a relation on a set \mathcal{A} then R\circ (S\circ T)=(R\circ S)\circ T.
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