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R is a relation between S0, ..., Sn-1 : <=>
R subset S0 x ... x Sn-1.
R is an n-ary relation : <=>
exists S_0, ..., S_n-1: R is a relation between S_0, ..., S_n-1;
R is an n-ary relation on S : <=>
R subset S x ... x S (cartesian product of n instances of S).
R is a relation on S : <=> R is a 2-ary ( binary) relation on S.
Set of tuples of related values.