chapter  9
47 Pages

Transitive Relations

Relations can be characterized in different ways. Many-one and one-one relations give rise to functions, and in particular to mappings, themselves establishing homomorphisms and isomorphisms. These will be discussed in §9.3, after considering the equivalence relations they characteristically generate. Equivalence relations are transitive and symmetric, and it is in terms of these features that relations are most illuminatingly classified. We can have relations that are symmetric but not transitive, such as spouse, other than, and different from; but of greater interest are the ordering relations, that is those that are transitive and asymmetric.