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 Post subject: Mathematica ProblemPosted: Mon, 15 Mar 2010 18:26:06 UTC
Hello there I was wondering if someone could give me a hand with a problem I'm having on Mathematica. I have the set X := {1,2,3,4}, and I have computed the Cartesian product of this set using Combinatorica.

I have inputted the two subsets
R:= {(1,2),(2,3),(3,4),(4,1)}
S:= {(2,1),(3,2),(4,3),(1,4)}

and I want to find the set

R o S = {(x,y) in X^2: there exists a unique z [depending on the pair (x,y)] such that (x,z) is in S and (z,y) is in R }

So i want mathematica to run through all the elements in X^2 and do a check to see if the condition in R o S is satisified. Is this possible? I have no idea how to define the set R o S or how to get mathematica to even run through all the 16 elements in X^2 to see if they satisfy certain conditions.

To clarify, (1,1) is in R o S because (1,4) is in S and (4,1) is in S. 4 is the unique element that joins x = 1 to y = 1. there is no other element except from 4 that does this.

Thanks for listening to my request and I hope someone can guide me on this.

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