vi.] THE INDIRECT METHOD OF INFERENCE. 91 



By symbolic statement the problem is instantly solved. 

 Taking 



A = member of board 



B = bondholder 



= shareholder 

 the premises are evidently 



A = ABc -I- AbC 



B = AB. 



The class C or shareholders may in respect of A and B be 

 developed into four alternatives, 



But substituting for A in the first and for B in the third 

 alternative we get 



C = ABCc -I- AB&C -|- AbC ] aABC -|- abC. 

 The first, second, and fourth alternatives in the above are 

 self-contradictory combinations, and only these ; striking 

 them out there remain 



G = AbC -I- abC = bC, 



the required answer. This symbolic reasoning is, I believe, 

 the exact equivalent of Mr. Venn's reasoning, and I do 

 not believe that the result can be attained in a simpler 

 manner. Mr. Venn adds that he could adduce other 

 similar instances, that is, instances showing the necessity 

 of a better logical method. 



Abbreviation of the Process. 



Before proceeding to further illustrations of the use of 

 this method, I must point out how much its practical 

 employment can be simplified, and how much more easy 

 it is than would appear from the description. When we 

 want to effect at all a thorough solution of a logical 

 problem it is best to form, in the first place, a complete 

 series of all the combinations of terms involved in it. If 

 there be two terms A and B, the utmost variety of 

 combinations in which they can appear are 



AB aB 



Ab ab. 



The term A appears in the first and second ; B in the first 

 and third ; a in the third and fourth ; and b in the second 

 and fourth. Now if we have any premise, say 

 A =B, 



