PERFORMANCE OE LOGICAL INFERENCE. 
507 
But as all our operations are directed only to distinguish the consistent and inconsistent 
combinations, we now join the highest to the second rank, and the third to the lowest, 
as follows : — 
{ A a a a 
B B b b 
C C C g 
f A A A a 
Combinations inconsistent with (1) or (2), or both . ,<B b b B 
[c C c c 
25. The problem is now solved, and it only remains to put any question we may 
desire. Thus if we want the description of the class A, we may raise out of the con- 
sistent combinations such as are As, and the sole remaining combination ABC gives 
the description required, agreeably to our former conclusion. To obtain the description 
of B, we unite the consistent combinations again and raise the As ; there will remain two 
combinations ABC and a B C, showing that B is always C, but that, so far as the con- 
ditions of the problem go, it may or may not be A. 
26. In considering such other kinds of propositions as might occur, we meet the case 
where two or more terms are combined together to form the subject or predicate, as in 
the example 
A B is C, 
meaning that whatever combinations contain both A and B, ought also to contain C. 
This case presents no difficulty; and to obtain the included combinations it is only 
necessary to raise out of the whole series of combinations the as and As, simultaneously 
or successively. The result, in whatever way 
we 
do it, 
is as 
follows : 
— 
f A 
A 
a 
a 
a 
a 
Excluded combinations .... 
. 
r 
b 
B 
B 
b 
b 
(c 
G 
C 
c 
C 
G 
f A 
A 
Included combinations . . .< B 
B 
(C c 
We may then remove such of the included combinations, i. e. A B c only, as may be 
inconsistent with the premise, and proceed as before. 
27. Had the predicate instead of the subject contained two terms as in 
A is B C, 
we should have required to raise the as and then lower the Vs and the As, in an exactly 
similar manner. 
28. The only further complication to be considered arises from the occurrence of the 
disjunctive conjunction or in the subject or predicate, as in the case 
A is B or C (or both). 
3 z 2 
