It is well known in set theory that the ordered pair can be represented by set systems like {{a}} or {{a} {a b}}. Either of these set systems can be combined to form the multisets {a} and {a a b}. This leads to the multiset theoretic definition of the ordered pair. This puts the element with the highest multiplicity first before the second element with less multiplicity. This is necessary so that the multiset corresponds to a set system so {a} corresponds to {{a}} and {a a b} coresponds to {{a} {a b}.
One immediate consequence of this fact is that all binary relations can be represented as sets of multisets. Well it is clear that graphs and preorders, both of which can be considered to be types of binary relations, can be represented as set systems, there are certain other binary relations that cannot be represented as set systems well all binary relations can be. The multiset theoretic definition of binary relations corresponds then to the set of combinational multisets of a set of kuratowski pairs which is a set of sets of sets.
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