# Types of Syllogisms

### changing minds .org

Syllogisms are arguments that take several parts, typically with two statements which are assumed to be true (or premises) that lead to a conclusion.

There are three major types of syllogism:

* Conditional syllogism: If A is true then B is true (If A then B).

* Categorical syllogism: If A is in C then B is in C.

* Disjunctive syllogism: If A is true, then B is false (A or B).

## Conditional Syllogism

The basic form of the conditional syllogism is: If A is true then B is also true. (If A then B). It appears through a major premise, a minor premise and a conclusion.

Example:

You are sad.

I am qualified to help people who are sad.

I can make you happy.

## Categorical Syllogism

The basic form of the categorical syllogism is: If A is part of C then B is a part of C. (A and B are members of C).

Example:

All New Yorkers are happy.

Some people live in New York.

Some people are happy.

## Disjunctive Syllogism

The basic form of the disjunctive syllogism is: Either A is true or B is true. (A exclusive-or B). Thus, if A is true, B is false, and if B is true, A is false. A and B cannot both by true.

Example:

Either you vote for me or you vote for disaster.

## The Rules of the Syllogism

There must be three terms.

The middle term must be distributed at least once.

No term may be distributed in the conclusion, if it was not distributed in the premise.

No conclusion may be drawn from two particular premises nor from two negative premises.

If one of the premises is negative, the conclusion must be negative.

These rules concern the validity of a syllogism, but NOT its truth. Truth is determined by whether or not we agree with the premises.

Testing Exercise 1.