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A part of B 
A part of not-B 
Not- A part of B 
Not- A part of uot-B. 
Other apparent varieties, such as B part of not- A, will be 
found equivalent to one or other of the above, equivalent laws 
being those which lead to the same possible combinations. 
The remaining two selections of combinations are found 
to correspond to the general form of law A=B expressing 
the coincidence of the classes A and B, as, for instance, the 
coincidence between equilateral and equiangular triangles. 
This form is capable of only one other logically distinct 
variety, that expressing the coincidence of A with the class 
not-B. Thus the solution of the inverse logical problem of 
two terms leads us to the conclusion that only two forms of 
relation can exist between two classes, namely, the relations 
of 'partial and complete coincidence , but these relations may 
exist in six different ways altogether, capable of expression 
in a still greater number of different propositions. 
The inverse problem of three terms is a far more complex 
matter, since the possible combinations are eight in number, 
and the selections of such combinations, the eighth power of 
two, or 256. Many of such selections involve self-contra- 
diction, but there appears to be no mode except exhaustive 
examination of ascertaining how many. By methods of 
inquiry fully described in the paper, it is shown that there 
cannot exist more than fifteen general types or forms of 
logical conditions governing the combinations of three 
classes of objects. Some of these forms of law, for instance 
A=ABC, expressing the inclusion of A in the class BC, are 
capable of as many as 24 variations; other forms of law 
admit 12, 8, or 6 variations. A remarkable and unique form 
is discovered in the proposition 
A - BC or not-B not-C, 
