AND MULTIPLICATION OP LOGICAL RELATIVES, 217 



By adding these four relatives to unity and to negative 

 unity, we obtain the eight following canonical equations. 

 It will be remembered that, as i is the symbol of identity, 

 the following equation is true, 



A=iA, 



whatever be the meaning of A. 



i+L =1. 5- -1+^ =0- 



i+L-' = i. 6. -i+L-' = o. 



i+N =0. 7- -1+^ =-i- 



i+M =U+U-\ 8. -i+M =-i. 



These are to be interpreted as follows, in syllogistic 

 form : — 



1 . A is identical with B ; 

 A is included in B ; 

 A and B are identical. 



2. A is identical with B ; 

 A includes B ; 



A and B are identical. 



3. A is identical with B ; 

 Nothing is both A and B ; 



One or both of the premises must be untrue. 



4. A is identical with B ; 

 Every thing is either A or B ; 

 Every thing is both A and B. 



5. A and B are the negatives of each other ; 

 A is included in B ; 



One or both of the premises must be untrue. 



6. A and B are the negatives of each other; 

 A includes B ; 



One or both of the j^re^uises must be untrue. 



