All cases of A being B are cases of C being D. .'. Whatever is not a case of A being B is not a case of C being D. This is the same as to argue-- All A is B, .'. All not-A is not-B, an erroneous form of immediate inference for which there is no special name, but which involves the vice of simple conversion of A, since 'All not-A is not-B' is the contrapositive, not of 'All A is B,' but of its simple converse 'All B is A.' § 759. The above-mentioned form of immediate inference, however (namely, the employment of contraposition without conversion), is valid in the case of the U proposition; and so also is simple conversion. Accordingly we are able, as we have seen, in dealing with a proposition of that form, both to deny the antecedent and to assert the consequent with impunity-- If A is B, then only C is D, .'. A not being B, C is not D; and again, C being D, A must be B. CHAPTER XXIII. _Of the Disjunctive Syllogism_. § 760. Roughly speaking, a Disjunctive Syllogism results from the combination of a disjunctive with a simple premiss. As in the preceding form, the complex proposition is regarded as the major premiss, since it lays down a hypothesis, which is applied to fact in the minor. § 761. The Disjunctive Syllogism may be exactly defined as follows-- A complex syllogism, which has for its major premiss a disjunctive proposition, either the antecedent or consequent of which is in the minor premiss simply affirmed or denied. § 762. Thus there are four types of disjunctive syllogism possible. _Constructive Moods._ (1) Either A is B or C is D. (2) Either A is B or C is D. A is not B. C is not D. .'. C is D. .'. A is B. Either death is annihilation or we are immortal. Death is not annihilation. .'. We are immortal. Either the water is shallow or the boys will be drowned. The boys are not drowned. .'. The water is shallow. _Destructive Moods_. (3) Either A is B or C is D. (4) Either A is B or C is D. A is B. C is D. .'. C is not D. .'. A is not B.