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# The general case

Definition 4.1.1   An ordered triple of sets where is called a binary relation between the elements of and the elements of . The set is called the domain of the relation, is the range and is the graph of the relation.

If , the relation is called the empty relation. For example, let be the set of children who learn in a given institution; suppose that the set is made of all the pairs of children where is a friend of . If , the social situation in this institution is very serious and needs help. The same kind of graphical representation we used for the cartesian product of two sets can be used here too, no point other than those of being displayed. For example, let and . If , the corresponding diagram is displayed on Figure 1(a).

Sometimes another kind of diagram is useful: we represent the domain and the range of the relation by Venn diagrams, then we draw an arrow from to for every pair in , as in Figure 1(b).

Notation 2   A binary relation is often denoted by a single letter (or symbol) like , , etc. With this notation we write instead of .

Next: Binary relations between elements Up: Binary relations Previous: Binary relations   Contents
root 2002-06-10