§ 730. On comparing these results with the converse by negation of each of the same propositions, A and 0, the reader will see that they differ from them, as was to be expected, only in being permuted. The validity of the inference may be tested, both here and in the case of conversion by negation, by reducing the disjunctive proposition to the conjunctive, and so to the simple form, then performing the process as in simple propositions, and finally throwing the converse, when so obtained, back into the disjunctive form. We will show in this manner that the above is really the contrapositive of the 0 proposition.
(O) Either A is B or C is sometimes not D.
= If A is not B, C is sometimes not D.
= Some cases of A not being B are not cases of C being D. (Some A is
not B.)
= Some cases of C not being D are not cases of A being B. (Some
not-B is not not-A.)
= If C is not D, A is sometimes not B.
= Either C is D or A is sometimes not B.
CHAPTER XX.
Of Complex Syllogisms.
§ 731. A Complex Syllogism is one which is composed, in whole or part, of complex propositions.