The method may be varied by bringing the propositions to the form
No X is Q1 or Q2 … or Qn,
or to the form
Nothing is Q1 or Q2 … or Qn,
then combining them as in section [476], and (if an affirmative solution is desired) finally obverting the result. It will depend on the form of the original propositions whether this variation is desirable.[508]
[508] This second method is analogous to that which is usually employed by Dr Venn in his Symbolic Logic. Both methods bear a certain resemblance to Jevons’s Indirect Method; but neither of them is identical with that method.
In an equational system of symbolic logic, a solution with regard to any term X generally involves a partial solution with regard to x also. In the employment of the above methods, x must be found separately. It may be added that the complete solutions for X and x sum up between them the whole of the information given 508 by the original data; in other words, they are, taken together, equivalent to the given premisses.[509]
[509] Having determined that All X is P and that All x is q, we may by contraposition bring the latter proposition to the form All Q is X, and it may then be found that P and Q have some alternants in common. These alternants are the terms which (in Boole’s system) are taken in their whole extent in the equation giving X ; and the solution thus obtained is closely analogous to that given by any equational system of symbolic logic.
The following may be taken as a simple example of the first of the above methods. It is adapted from Boole (Laws of Thought, p. 118).
“Given 1st, that wherever the properties A and B are combined, either the property C, or the property D, is present also, but they are not jointly present; 2nd, that wherever the properties B and C are combined, the properties A and D are either both present with them, or both absent; 3rd, that wherever the properties A and B are both absent, the properties C and D are both absent also; and vice versâ, where the properties C and D are both absent, A and B are both absent also. Find what can be inferred from the presence of A with regard to the presence or absence of B, C, and D.”