THE INDIRECT METHOD OF INFERENCE. 117 



In these combinations the only A which appears is 

 joined to c, and similarly C is joined to a, or A is incon- 

 sistent with C. 



A more complex argument, also given by De Morgan f , 

 contains five terms, and is as stated below, except that I 

 have altered the letters. 



' Every A is one only of the two B or C ; D is both B 

 and C, except when B is E, and then it is 

 neither ; therefore no A is D/ 



A little reflection will show that these premises are 

 capable of expression in the following symbolic forms 

 A = ABc + AJO, (i) 



De = DeBC, (2) 



DE=DE6c. (3) 



As five letters, A, B, C, D, E, enter into, these premises it 

 is requisite to treat their thirty-two combinations, and it 

 will be found that fourteen of them remain consistent with 

 the premises, namely 



ABcdE " aRCVe abCdE 



KEcde aBCdE abCde 



AbCdE aRCde abcDft 



AbCde aBcdE abcdft 



aBcde abode. 



Now if we examine the first four combinations, all of 

 which contain A, we find that they none of them contain 

 D ; or again if we select those which contain D, we have 

 only two, thus 



D = aBCDe I a&cDE. 



Hence it is clear that no A is D, and vice versa no D is A. 

 We might also draw many other conclusions from the 

 premises ; for instance 



DE = a&cDE, 

 or D and E never meet but in the absence of A, B, and C. 



f 'Formal Logic/ p. 124. 



