§ 770. If no stress be laid on the transition from disjunctive hypothesis to fact, the disjunctive syllogism will run with the same facility as its predecessor into the moulds of immediate inference.
§ 771.
Denial of Antecedent. Subalternation.
Either A is B or C is D, Every case of A not being B
is a case of C being D.
.'. A not being B, C is D. .'. Some case of A not being B
is a case of C being D.
§ 772.
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.