134 THE PRINCIPLES OF SCIENCE. 



are those which altogether remove any one or more letter- 

 terms from the Abecedarium. 



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 = Ab B = aB 



A = b a- B 



A-BC a = b\c 



A = AB t AC b = ab t AbC 



A I B = C t D ab = cd 



At c = B t d aC = bD 



, A = ABtACl 



A = ABc I Ab(j A -r, . ,, 

 AB = ABc 



A = Bl 

 A= CJ 

 A = AC 

 B = A t aBC 



A = ABCD. 



