227 
of Edinburgh, Session 1878 - 79 . 
15. Suppose that we have given the two equations 
s m A = B, and 
o 
II 
<1 
CO S 
then 
B = s„-C , 
*« 
and 
C = s„— B. 
The expression s m — denotes the relationship of sons of the same 
S n 
father. 
If m = n , then B = C . 
Thus the general analytical expression for brother includes oneself. 
16. De Morgan remarks on the difficulty commonly experienced 
by persons of putting together two (not to say more than two) con- 
ditions about relationship, that is, of deducing the conclusion from 
two given data which really afford a conclusion. ' He was accustomed 
to propound the following story, among others, as a test : — An 
abbess observed that an elderly nun was often visited by a young 
gentleman, and asked what relation he was. “ A very near rela- 
tion,” answered the nun; “his mother was my mother’s only 
child.” 
Let G denote the gentleman, and JST the nun. Then the condi- 
tions given are — 
-G = sbr, and 8=1. 
Since 8 = 1, 8g = 1 (Art 1 5), 
-G = N 
(T 
or G = crbT . 
That is, the gentleman was the son of the nun. 
When the visitor is not said to be young, the problem presents still 
greater difficulty to the ordinary intelligence. 
17. Suppose s 2 s,A. = s 2 — y-M , 
(A j 
that is, the second son of the fourth son of A is identical with 
the second son of the father of a man his first son who was the 
father of a woman his first daughter M. 
