346 PROF. W. STANLEY JEVONS ON 



then there will be three possible classes to be determined^ 



namely^ 



AB, 



«B, 



ab, 



and we shall require three assigned quantities. If we have 

 (U) = whole number of objects^ with (A) and (B);, then 



(AB) = (A) 



(aB) = (B)-(A) 

 («5) = (U)-(B). 



21. If with two terms_, A and B_, the logical condition 

 be A=:B^ there will remain two classes only^ AB and aby 

 and two assigned quantities only will be required. The 

 same would happen with any of tbe conditions A=b, 

 c5=B, or a=^b. 



22. In any problem involving three terms or classes of 

 things, say A_, B, and C, there arise eight conceivable 

 classes, the numbers of which may have to be determined. 

 Various logical conditions, however, greatly reduce the 

 numbers. Thus the two conditions 



A=B = C 



leave only two possible classes, ABC, and abc. 

 The two conditions 



A=ABandB = BC 



leave four classes, 



ABC, «BC, abC, and abc. 



23. The two conditions A is B or C, but B cannot be C, 

 symbolically expressed 



A=ABlAC, B = Bc, 



leave five classes, 



ABc, KbC, oBc, abC, abc. 



