CHAP. VII.] OF ELIMINATION. 105 



what in the common logic is called conversion by contraposition, 

 or negative conversion.* 



Ex. 2. Taking the Proposition, " No men are perfect," as 

 represented by the equation 



wherein y represents " men," and x " perfect beings," it is re- 

 quired to eliminate v, and find from the result a description both 

 of perfect beings and of imperfect beings. We have 



y-9(l-):-0. 



Whence, by the rule of elimination, 



fcf-(l-*)}xy-0, 

 or y - y (1 - x) = 0, 



or yx = ; 



which is interpreted by the Proposition, Perfect men do not exist. 

 From the above equation we have 



# = - = -(l-2/)by development ; 



whence, by interpretation, No perfect beings are men. Simi- 

 larly, 



which, on interpretation, gives, Imperfect beings are all men with 

 an indefinite remainder of beings, which are not men. 



11. It will generally be the most convenient course, in the 

 treatment of propositions, to eliminate first the indefinite class 

 symbol v, wherever it occurs in the corresponding equations. 

 This will only modify their form, without impairing their signifi- 

 cance. Let us apply this process to one of the examples of 

 Chap. iv. For the Proposition, " No men are placed in exalted 

 stations and free from envious regards," we found the expression 



y = v (1 - xz), 



and for the equivalent Proposition, " Men in exalted stations are 

 not free from envious regards," the expression 

 yx = v(\- z); 



* Whately's Logic, Book II. chap. H. sec. 4. 



