220 MR. JOSEPH JOHN MURPHY ON ADDITION 



3. A=L-^B; or B is A. 

 Denied by 



4. A=Z~'Bj or some B is not A. 



5. A=iVB ; or no A is B ; or no B is A. 

 Denied by 



6. A=nB ; or some A is B ; or some B is A. 



7. A = ikf B ; or every thing is either A or B. 

 Denied by 



8. A=mB ; or something is neither A nor B. 



Each of these eight relatives has its form with zero 

 index, making altogether sixteen terms, which combine 

 into 256 syllogisms ; but of these only 76 are conclusive. 

 They are set forth in the following table. As before, the 

 multipliers are in the left-hand column, and the multi- 

 plicands in the top line. The terms are so arranged, 

 that if the table be folded by the middle either vertically 

 or horizontally, each of the four terms 



L L-' ' N M 



will rest on the term denying it ; and each of the four 

 terms 



will rest respectively on 



The numbers in the top left-hand corner of each square 

 are those of the multiplier and the multiplicand which 

 form the product in that square ; and the numbers in the 

 bottom right-hand corner are those of the multiplier and 



