134 THE PRINCIPLES OF SCIENCE. 



are those which altogether remove any one or more letter- 

 terms from the Abecedariurn. 



What is true of single propositions applies also to 

 groups of propositions, however large or complicated ; 

 that is to say, one group may be equivalent, inferrible, 

 consistent, or contradictory as regards another, and we 

 may similarly compare one proposition with a group of 

 propositions. 



To give in this place illustrations of all the four kinds 

 of relation would require much space : as the examples 

 given in previous sections or chapters may serve more or 

 less to explain the relations of inference, consistency, and 

 contradiction, I will only add a, few instances of equivalent 

 propositions or groups. 



In the following list each proposition or group of propo 

 sitions is exactly equivalent in meaning to the correspond 

 ing one in the other column, and the truth of this state 

 ment may be tested by working out the combinations of 

 the Abecedarium, which ought to be found exactly the 

 same in the case of each pair of equivalents. 

 A = A6 B = aB 



A = b a = B 



A = BC a = b\c 



A = AB I AC b = ab I A&C 



A-|-B = C-|-D ab = cd 



A I c = B I- d aC = bV 



A = ABI AC 



A = ABc I A6C A .~ 



AB = ABc 



A = Bl A = B 



B = CJ A- C 



A - ABl A = AC 



B - BCJ B = AlaBC 



A = ABi 



A - AC I A = ABCD. 



A = AD-I 



