TYPES OF COMPOUND STATEMENT. 83 



complementary statements will also be similar; and, con- 

 sequently, for every type of n-fold statement there is a 

 complementary type of i6— w-fold statement. It follows 

 that we need only enumerate the types as far as the eighth 

 order ; for the types of more than eightfold statement will 

 already have been given as complementary to types of lower 

 orders. Every eightfold statement is complementary to 

 an eightfold statement ; but these are not necessarily of 

 the same type. 



3. One mark A BCD may be converted into another 

 AbCd hj interchanging one or more of the classes A, B, 

 C, D with its complementary class. The number of such 

 changes is called the distance of the two marks. Thus in 

 the example given the distance is 2. In two similar com- 

 pound statements the distances of the marks denied must be 

 same ; but it does not follow that when all the distances are" 

 the same the two statements are similar. There is, how- 

 ever, as we shall see, only one example of two dissimilar 

 statements having the same distances. When the distance 

 is 4, the two marks are said to be obverse to one another, 

 and the statements denying them are called obverse state- 

 ments — as ABCD, abed, or, again, AbCd, aBcD. 

 When any one mark is given (called the origin), all the 

 others may be grouped in respect of their relations to it as 

 follows : — Four are at distance one from it, and may be 

 called proximates ; six at distance two, and may be called 

 mediates; four at distance three, and maybe called ultimates. 

 Finally, the obverse is at di stance /owr. 



«BOD ahCT> Abed 



AhcJ) I AhCd 



\ / 



ABCc? — ABCD — A6CD V ahcD — abed — a^ed 



a B cD^ I \^BC<^ 

 ABcD ABc<^ ahQd 



Origin and 4 proximates. 6 mediates. Obverse and 4 ultimates, 



g2 



