The problem:
I have a relation R where
domain set is: dom R = {A,B,C}, and
range set is: ran R = {1,2,3}.
The relations (maplets) are:
{A>1,A>3,B>2,B>3,C>1,C>3}

The following sets would be performed, if we use at most once every element
from each side of the relationship, within each new set. (E.g. {A>2,B>1} is
ok but {A>2,A>3,C>3} is not ok because A and 3 is being twice in the set).

We have:
first {A>1,B>2,C>3}
second {A>1,B>3} (not C3 because 3 is used)
third {A>1,C>3}
fourth {A>3,B>2,C>1}
etc.

I try to capture the sets with the most number of elements (first and fourth
line, that have 3 elements each) and be able to store these somehow, for
further manipulation.

I have spent long time with this problem, and I looked into the association
problem in operations management and in maths, but still, I couldn?t create
any algorithm.

Any help is appreciated.
Jim.