A syllogism is a form of mediate inference in which a conclusion is drawn from the joint assertion of two premises. In a syllogism, when both the premises and the conclusion are categorical propositions, it is called pure-categorical syllogism.
In the like manner, a syllogism is a pure-hypothetical syllogism when all its constituent propositions are hypothetical propositions. Pure-alternative and pure-disjunctive syllogisms are not in general valid arguments.
In a syllogism, when all the constituent propositions are not of one kind, we call it a mixed syllogism. In a mixed-syllogism the constituent propositions are not of one particular type. There can be four different types of mixed syllogism like (1) Hypothetical-Categorical, (2) Disjunctive-Categorical, (3) Alternative-Categorical syllogisms, and (4) Dilemma.