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Math Help - Relations, wrecking my head!!!???

  1. #1
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    Relations, wrecking my head!!!???

    Let R be the relation {(0,0),(2,1),(1,3),(3,1),(3,0),(0,2),(2,3),(3,3)} defined on the set X ={(0,1,2,3)}.

    I have drawn the digraph and answered the first q whether its symmetric,reflexive,antisymmetric or transitive(easily enough)
    Need help with this Q though:

    Qustion:By considering each element of R, determine the relation R' on X with the smallest number of elements satisfying;
    (a) R subset R'
    (b) R' is symmetric
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  2. #2
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    Quote Originally Posted by kodirl
    Let R be the relation {(0,0),(2,1),(1,3),(3,1),(3,0),(0,2),(2,3),(3,3)} defined on the set X ={(0,1,2,3)}.

    Qustion:By considering each element of R, determine the relation R' on X with the smallest number of elements satisfying;
    (a) R subset R'
    (b) R' is symmetric
    Note that R is not symmetric. How do you need to "fix" R to make it symmetric? You need to make (a,b)\in R\leftarrow\rightarrow (b,a)\in R.
    Okay, look at the elements you have and switch their first and second members and attach them to R'.
    \{ (0,0),(2,1),(1,2),(1,3),(3,1),(3,0), (0,3),(0,2),(2,0),(2,3),(3,2),(3,3) \}
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