§ 732. Though there are only two kinds of complex proposition, there are three varieties of complex syllogism. For we may have

(1) a syllogism in which the only kind of complex proposition
employed is the conjunctive;

(2) a syllogism in which the only kind of complex proposition
employed is the disjunctive;

(3) a syllogism which has one premiss conjunctive and the other disjunctive.

The chief instance of the third kind is that known as the Dilemma.

Syllogism
___________________|_______________
| |
Simple Complex
(Categorical) (Conditional)
_____________________|_______________
| | |
Conjunctive Disjunctive Dilemma
(Hypothetical)

The Conjunctive Syllogism.

§ 733. The Conjunctive Syllogism has one or both premisses conjunctive propositions: but if only one is conjunctive, the other must be a simple one.

§ 734. Where both premisses are conjunctive, the conclusion will be of the same character; where only one is conjunctive, the conclusion will be a simple proposition.

§ 735. Of these two kinds of conjunctive syllogisms we will first take that which consists throughout of conjunctive propositions.