334 PROF. W. STANLEY JEVONS ON 



total number of electors is equal to the number of borough^ 

 county, and university electors added together ; for some 

 men may be found in two or three of the classes. 



8. This difficulty,, however, is avoided with great ease ; 

 for we need only develop each alternative into all its 

 possible subclasses and strike out any subclass which 

 appears more than once, and then convert into numbers. 



Thus, from 



A=BI-C 

 we get 



A = BC'\'Bc\'BC'\'bC; 



but striking out one of the terms BC as being superfluous, 



we have 



A=BClBc| ^»C. 



The alternatives are now strictly exclusive, or devoid of 

 any common part, so that we may draw the numerical 

 equation 



(A) = (BC)-h(Bc)-f (5C). 



Thus, if A = elector, 



B= borough elector, 

 C = county elector, 

 D = university elector, 



we may from the proposition, 



A=B.|.C|.D 

 draw the numerical equation 



(A) = (BCD) + (BC^) + (BcD) + (Bc^) + [bCD) + (bCd) 

 + {bcJ)). 



9. The process of development employed above is the 

 great peculiarity of Prof. Boole^s system of logic, and that 

 which I have adopted. It depends upon the primary law 

 of thought, usually called the Law of Excluded Middle, 

 but which I prefer to call the Laiv of Duality. Whatever 



