1. ## 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

2. 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'.
$\{ (0,0),(2,1),(1,2),(1,3),(3,1),(3,0),$ $(0,3),(0,2),(2,0),(2,3),(3,2),(3,3) \}$