of the Privative Propositions of Logic 89 



By Ackl, SylL, I- (1), 



(b) By lemma to Syll., q/q\s/q; by Perm, and Syll, q/q Iq/s. 

 Hence, q/q \ L/L ; by Perm., L/L \ q/q. 

 Now, by Syll. : 



L/L 1 q/q .D:q\L/L.D . L/L | L/L. 



By 1-6, h a, and Taut. -, result. We can now complete the proof 

 of ' Association.' 



Association, p \ q/r \ q \ p/r 



Dem. : By Syll., /) | q/r . D : q/r \r .\. p/r 

 By Syll. twice, h Lemma, result. 



Summation, qDr .D : pvq .D .pv r 



Dem. : By Syll., Assoc, 



q \s .D : p\ q/r . D . p\s (1) 



^ . s/s, q, p/p , 



By (1) — ^-^, result. 



-^ s, r, p 



Theorems Equivalent to the Definitions of p Dq, p . q, 

 IN Principia. 



p"^ q • 3 . ^pv q, and reciprocal theorem. 

 That is, p I q/q . D .p/p \ q/q. 



Bern. : Taut., and Syll. 



sis D 



Reciprocal theorem by Add. -^ — — , and Syll. 



.9, p 



p\ q ."D . ^p V ~ q, and reciprocal theorem. 

 That is, j9 1 5 . D . p/p \ q/q. 



