# Meaning of Disjunctive Syllogism & Disjunctive Syllogism Example

Table of Contents

## Disjunctive Syllogism

**What is Disjunctive Syllogism?**

**Disjunctive Syllogism** is a logical argument that uses two premises and one conclusion. The first premise states that either the subject or object in a scenario can be true, but not both. The second premise states that the other of these options must also be true. The last part or third premise explains why this is so, which is then followed by the conclusion stating what has been proven to be correct based on all three premises.

Disjunctive Syllogism is an example of how logic can be used to determine the truth or falsity of a proposition.

It is important to understand this concept because it will help you learn other types of logical arguments, such as **conditional syllogism**. A disjunctive syllogism consists of three statements; two premises and a conclusion.

The two premises are called “**disjunct,**” and they must both be true for the conclusion to follow from them logically.

It is a **syllogistic form of argument** that has three main parts:

- The major premise
- The minor premise
- The conclusion.

It is also an example of a valid argument with true premises.

Disjunctive Syllogism is an example that shows how to use syllogistic logic. By understanding this example you can understand how to use the syllogism in your own arguments and reasoning.

It is also an example of the more general class known as **Sorites arguments**, which are also called **Fence-Sitting arguments. **This is a logical form that has been used for centuries.

It can be confusing to use at first, but once you have learned how to use it, you will be able to spot many different types of logical fallacies and arguments filled with them.

### Conditional Syllogism

A conditional syllogism is a type of logical argument that has three parts:

- The major premise: The major premise states what will happen if something else happens (or does not happen)
- The minor premise: the minor premise states what would have to be true for the consequence in the major premise to take place (or not take place).
- The conclusion: The conclusion follows from both premises.

A conditional syllogism is a form of deductive reasoning in which the conclusion is **conditional on two premises**. The first premise is called the “major” premise, and the second, the “minor” premise. In order for the conclusion to be valid, both premises must be true.

#### Conditional Syllogism Examples

Conditional syllogisms follow a logic pattern; “**If A is true, then B is true.” **Conditional syllogism examples are also known as **hypothetical syllogisms** because the argument is not always valid.

**Conditional syllogisms examples: **

- All men are mortal
- Socrates is a man
- Therefore, Socrates is mortal

It follows that if All men are mortal and Socrates is a man, then it is logical that Socrates is mortal.

In a **syllogism**, the more general premise is called the major premise (“All men are mortal”), minor premise (” Socrates is a ma”). The conclusion joins the logic of the two premises (“Therefore, Socrates is mortals”).

## Disjunctive Syllogism Example

A disjunctive syllogism is a type of logical argument in which the conclusion is drawn from two or more premises, at least one of which must be false.

The form of this kind of argument can be represented as “A or B,” where A and B are statements that may both be true but not necessarily.

**Disjunctive Syllogisms Example 1: ** If it’s raining outside, then you’re wearing your boots; It’s not raining outside, so you’re not wearing your boots.

**Disjunctive Syllogisms Example 2**

This type of syllogism has a “**disjunction**” as a premise, that is, an “either-or” statement.

Example example:

- Either my sibling is a sister, or my sibling is a brother.
- My sibling is not a sister.
- Therefore, my sibling is a brother.

## Disjunctive Syllogism Fallacy

A syllogism is a form of logical argument that has two premises and one conclusion.

Disjunctive Syllogism is when the second premise in a syllogism is false or irrelevant to the conclusion.

Disjunctive Syllogism Fallacy is the incorrect assumption that a disjunction of two statements must be true if one or both of them are false. This fallacy can take many forms, including:

- “Either you’re telling the truth, or you’re lying.”
- “You have to either do this now or later.”

### Disjunctive Syllogism Fallacy Example

An example of Disjunctive Syllogism Fallacy would be “All cats are animals, but not all animals are cats.”

### Disjunctive Syllogism Summary

A **disjunctive syllogism** is a formal logical argument that has two premises, one of which must be false.

The first premise states the conclusion to be proved, and the second premise states an impossible situation.

If both premises are true, then the first premise’s statement can only be false if both statements can’t be true at once.