THE LOGIC OF RELATIVES. 



d. Fourth, simple relatives are divisible into those which contain elements of the 



K r 



form (A:A) and those which do not. The former express relations iteli a> .. thii 

 may have to itself, the latter (as cousin of—, hater of—) relations which nothii 

 can have to itself. The former may be termed self -relat ins, the latter nl -, fin 

 All copulatives are self-relatives. 



e. The fifth division is into relatives some power (i. e. repeat < I pi duet) of which 

 contains elements of the form (A:A), and tho^e of which this is not tine. The i rm r 

 I term cyclic, the latter non-cyclic relatives. „\< an example of the former, take 



(A : B)^(B ; A)-t(C:D) + (D:E) + (E : C). 



The product of this into itself is" 



(A:A)-k(B : B)^(C : E)-MD : C) + (i;:D 



The third power is 



. (A:B)-fr(B:A)-t(C:C)-t(D:D)-t(E:K, 



The fourth power is 



(A:A)H F (B:B)-| r (C:D)H r (D:K)-| r (E:C). 



The fifth power is 



(A:B)-t(B:A)-t(C:E>-t(B:C)-t(E:I> 



The sixth power is 



(A:A)-t(B:B)-t(C:C)-t(B:B) + (E : E) 







where all the terms are of the form (A: A). Such relatives, as con n of — , arc 



cyclic. All equiparants are cyclic 



/. The sixth division is into relatives no power of which is zero, and relativ me 

 power of which is zero. The former may be termed inexh<ui,fible, the latter exh 4 

 ble. An example of the former is "spouse of -," of the latter, "husband of -." 



All cyclics are inexhaustible. 



g. Seventh, simple relatives may be divided into those whose products into hem- 

 selves are not zero, and those whose product* into themselves are zero. The former 

 may be termed repeating, the latter, non-repeating relatives. All inexhaustible rela- 



tives are repeating. 



/, Repeating relative, may be divided (after De Morgan) into those whose product* 

 into themselves are contained under themselves, and those of winch tb» - not true. 

 The former are well named by De Morgan tramilke, the latter itlmm* i A" *•* 

 sitives are inexhaustible ; all copulatives are transitive ; and all trans.tn e eqmparan* 

 are copulative. The class of transitive equiparants has a character, that of bemg 



self-relatives, not involved in the definitions of the terms. 



