_Denial of Consequent_. Conversion by Contraposition + Subalternation. Either A is B or C is D. All cases of A not being B are cases of C being D. .'. C not being D, A is B .'. All cases of C not being D are cases of A being B. .'. Some case of C not being D is a case of A being B. § 773. Similarly the two invalid types of disjunctive syllogism will be found to coincide with fallacies of immediate inference. § 774. _Affirmation of Antecedent_. Contraposition without Conversion. Either A is B or C is D. All cases of A not being B are cases of C being D. .'. A being B, C is not D .'. All cases of A being B are cases of C not being D. § 775. The affirmation of the antecedent thus comes under the formula-- All not-A is B, .'. All A is not-B, a form of inference which cannot hold except where A and B are known to be incompatible. Who, for instance, would assent to this?-- All non-boating men play cricket. .'. All boating men are non-cricketers. § 776. _Affirmation of Consequent_. Simple Conversion of A. Either A is B or C is D. All cases of A not being B are cases of C being D. .'.C being D, A is not B. .'. All cases of C being D are cases of A not being B. § 777. We may however argue in this way-- Conversion of A per accidens. Either A is B or C is D. All cases of A not being B are cases of C being D. .'. C being D, A is sometimes B. .'. Some cases of C being D are cases of A not being B. The men who pass this examination must have either talent or industry. .'. Granting that they are industrious, they may be without talent. CHAPTER XXVI. _Of the Mixed Form of Complex Syllogism_. § 778. Under this head are included all syllogisms in which a conjunctive is combined with a disjunctive premiss. The best known form is _The Dilemma_. § 779. The Dilemma may be defined as-- A complex syllogism, having for its major premiss a conjunctive proposition with more than one antecedent, or more than one consequent, or both, which (antecedent or consequent) the minor premiss disjunctively affirms or denies. § 780. It will facilitate the comprehension of the dilemma, if the following three points are borne in mind-- (1) that the dilemma conforms to the canon of the partly conjunctive syllogism, and therefore a valid conclusion can be obtained only by affirming the antecedent or denying the consequent; (2) that the minor premiss must be disjunctive;