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Math Help - Relations Question

  1. #1
    Newbie Halmos Rules's Avatar
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    Relations Question

    Suppose R and S are two reflexive and symmetric relations. Prove that RoS is reflexive and symmetric.

    This exercise was in an exam i took a couple of days ago. I could prove that RoS is reflexive, but i couldn't prove it is symmetric ( In fact i tried to prove that RoS is symmetric iff RoS=SoR). Any help would be greatly appreciated.
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  2. #2
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    On the set X = \left\{ {a,b,c} \right\} define relations
    \begin{gathered}<br />
  S = \left\{ {(a,a),(b,b),(c,c),(a,b),(b,a)} \right\} \hfill \\<br />
  R = \left\{ {(a,a),(b,b),(c,c),(c,b),(b,c)} \right\} \hfill \\<br />
  R \circ S = \left\{ {(a,a),(b,b),(c,c),(a,b),(b,a),(a,c),(c,b),(b,c)} \right\} \hfill \\<br />
  (a,c) \in R \circ S \hfill \\<br />
  (c,a) \notin R \circ S \hfill \\ <br />
\end{gathered}
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