1. Syllogisms and Three Types of Hypothetical Syllogisms
Logical Reasoning
Syllogisms and Three Types of Hypothetical Syllogisms

2. Definition of A Syllogism
A syllogism is a deductive argument presented in the form of two supporting premises and a conclusion. Premises and conclusion will be presented on separate lines with the conclusion last.

3. Two Types of Syllogisms
Hypothetical Syllogisms, is a form of deductive arguments that contain two premises at least one of which is a hypothetical or “if…., then …..” statement.
Categorical Syllogisms, is a deductive argument, in which categories or sorts things into specific classes, such as mammals, students, or countries. It is composed of a conclusion, two premises and three terms, each of which occurs exactly twice in two of the three propositions.

4. Three Types of Hypothetical Syllogisms
Modus Ponens , is a hypothetical syllogism in which the antecedent premise is affirmed by the consequent premise.
Example: If A (antecedent), then B (consequent). A.
Therefore, B.
If I get the raise at work, then I will pay off my debt.
I got the raise at work.
Therefore, I will pay off my debt.

5. Three Types of Hypothetical Syllogisms
Modus Tollens, is a hypothetical syllogism in which the second premise denies the consequent, and the conclusion denies the truth of the antecedent.
Example If A (Ancedent), then B (Consequent).
Not B.
Therefore, Not A.
If Jim is a lawyer, then he went to law school.
Jim did not go to law school.
Therefore, Jim is not a lawyer.

6. Three Types of Hypothetical Syllogisms
Chain Arguments, are hypothetical arguments in which three or more conditional premises are linked together.
Example:
If A, then B.
If B, then C.
If C, then D.
Therefore, A, then D.