§ 701. So far we have treated of inference, or reasoning, whether mediate or immediate, solely as applied to simple propositions. But it will be remembered that we divided propositions into simple and complex. I t becomes incumbent upon us therefore to consider the laws of inference as applied to complex propositions. Inasmuch however as every complex proposition is reducible to a simple one, it is evident that the same laws of inference must apply to both. § 702. We must first make good this initial statement as to the essential identity underlying the difference of form between simple and complex propositions. § 703. Complex propositions are either Conjunctive or Disjunctive (§ 214). § 704. Conjunctive propositions may assume any of the four forms, A, E, I, O, as follows-- (A) If A is B, C is always D. (E) If A is B, C is never D. (I) If A is B, C is sometimes D. (O) If A is B, C is sometimes not D. § 705. These admit of being read in the form of simple propositions, thus-- (A) If A is B, C is always D = All cases of A being B are cases of C being D. (Every AB is a CD.) (E) If A is B, C is never D = No cases of A being B are cases of C being D. (No AB is a CD.) (I) If A is B, C is sometimes D = Some cases of A being B are cases of C being D. (Some AB's are CD's.) (O) If A is B, C is sometimes not D = Some cases of A being B are not cases of C being D. (Some AB's are not CD's.) § 706. Or, to take concrete examples, (A) If kings are ambitious, their subjects always suffer. = All cases of ambitious kings are cases of subjects suffering. (E) If the wind is in the south, the river never freezes. = No cases of wind in the south are cases of the river freezing. (I) If a man plays recklessly, the luck sometimes goes against him. = Some cases of reckless playing are cases of going against one. (O) If a novel has merit, the public sometimes do not buy it. = Some cases of novels with merit are not cases of the public buying. § 707. We have seen already that the disjunctive differs from the conjunctive proposition in this, that in the conjunctive the truth of the antecedent involves the truth of the consequent, whereas in the disjunctive the falsity of the antecedent involves the truth of the consequent. The disjunctive proposition therefore Either A is B or C is D may be reduced to a conjunctive If A is not B, C is D, and so to a simple proposition with a negative term for subject. All cases of A not being B are cases of C being D. (Every not-AB is a CD.)