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Where possible, a relation R is implemented as <math>\{(x,y) \mid x R y\}</math> (which may
be written as <math>\{z \mid \pi_1(z) R \pi_2(z)\}</math>). In [[ZFC]], any relation which
has ___domain a subset of a set A and range a subset of a set B will be a set, since the cartesian product <math>A \times B = \{(a,b) \mid a \in A \wedge b \in B\}</math> is a set (being a
subclass of <math>P(P(A \cup B))</math>) and Separation provides for the existence of <math>\{(x,y)\in A \times B \mid x R y\}</math>. In [[NFU]], some relations with global scope
(such as equality and subset) are implemented as sets.
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