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 -I- A0, " (i) 



De = DeBC, (2) 



DE=DE&c. (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 



ABccE aBCDe a&CcZE 



ABccfe aBCcE abCde 



A6CcE aBCde a&cDE 



AbGde - aBccffi abcdEt 



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 versd 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, 1 p. 124. 



