—as, in the case of spouse, one term of the relation belongs to the class of males and one to the class of females. In such a case, the relation with its domain confined to
will be asymmetrical, and so will the relation with its domain confined to
. But such cases are not of the sort that occur when we are dealing with series of more than two terms; for in a series, all terms, except the first and last (if these exist), belong both to the domain and to the converse domain of the generating relation, so that a relation like husband, where the domain and converse domain do not overlap, is excluded.
The question how to construct relations having some useful property by means of operations upon relations which only have rudiments of the property is one of considerable importance. Transitiveness and connexity are easily constructed in many cases where the originally given relation does not possess them: for example, if
is any relation whatever, the ancestral relation derived from