The Principles of Mathematics (1903)

§ 97

We can form the logical sum and product of two relations or of a class of relations exactly as is the case of classes, except that here we have to deal with double variability. In addition to these ways of combination, we have also the relative product, which is in general non-commutative, and therefore requires that the number of factors should be finite. If R, S be two relations, to say that their relative product RS holds between two terms x, z is to say that there is a term y to which x has the relation R, and which itself has the relation S to z. Thus brother-in-law is the relative product of wife and brother or of sister and husband; father-in-law is the relative product of wife and father, whereas the relative product of father and wife is mother or step-mother.(§ 97 ¶ 1)