# Deductive Reasoning: Examples & Definition

Deductive reasoning involves drawing conclusions from specific statements called premises. Learn more about deductive reasoning and test your knowledge with a quiz.

## Defining Deductive Reasoning

Suppose that you wanted to find a fruit to eat. You look through the refrigerator and find a celery stick, a Granny Smith, and a cup of beans. You know that neither celery nor beans are fruits. You also know that all apples are fruits, and a Granny Smith is an apple. Therefore, the Granny Smith has to be a fruit.

This is an example of syllogism, a form of deductive reasoning. Deductive reasoning is a type of logic where general statements, or premises, are used to form a specific conclusion. The other type of deductive reasoning is conditional reasoning.

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## Syllogisms

Syllogisms are deductive arguments that are written in the form:

A is B
C is A
Therefore, C is B

Let’s take the example above. If we broke down the syllogism into premises and conclusions, we would get:

Premise: All apples are fruits.
Premise: A Granny Smith is an apple.
Conclusion: Therefore, a Granny Smith is a fruit.

According to the first premise, all items that are classified as apples are also classified as fruits. According to the second premise, Granny Smith is classified as an apple. The first premise is a general statement, while the second premise refers to a specific case. The conclusion says that a Granny Smith has to be a fruit because of its inherent properties as an apple. This deductive argument is also valid, which means that the conclusion necessarily follows from the premises. So, does a valid deductive argument mean that the premises and conclusions are true? Suppose I formed this deductive argument:

Premise: All dogs have long ears.
Premise: Puddles is a dog.
Conclusion: Therefore, Puddles has long ears.

Given the premises that all dogs have long ears and Puddles is a dog, it is logical to assume that Puddles has long ears. After all, in this example, long ears are an inherent quality of dogs. The argument is valid. Does that mean it is also true?

Not all dogs have long ears. Certain breeds, like Yorkies or pugs, have small ears. Because the conclusions are based off the premises and one of the premises is not true, it follows that the conclusion is not true, even though it is valid. You can see from this example that if one of the premises is not true, the conclusion is also not true.

## Conditional Reasoning

So what is conditional reasoning? Conditional reasoning uses if-then statements that are true to form a true conclusion. The conclusion can be either valid or invalid, even though the premises are true.

This chart shows the four types of conditional reasoning:

You can see that affirming the antecedent and denying the consequent are the only valid forms of conditional reasoning. That is, the conclusions logically follow from the premises.

Let’s look at the example of affirming the consequent. We know that a Yorkie is a type of dog. However, we also know that there are other types of dogs beside Yorkies. Therefore, the conclusion that if it is a dog, then it is a Yorkie is false, even though the premises are true.

Let’s look at the example of denying the antecedent. Just because it is not a Yorkie, it does not follow that it is not a dog. For example, it could be a poodle, which would still classify as a type of dog. Because a Yorkie is only one of several possibilities that could be classified as a dog, the conclusion is incorrect.

## Lesson Summary

Deductive reasoning is a type of logical argument that involves drawing conclusions from premises. Syllogisms and conditional reasoning are the two types of deductive reasoning. There are four types of conditional reasoning, but only affirming the antecedent and denying the consequent are valid. Affirming the consequent and denying the antecedent are invalid forms of conditional reasoning.

## Learning Outcomes

When you are finished, you should be able to:

• Summarize what deductive reasoning is
• Name and describe the two types of deductive reasoning
• Determine whether a deductive argument is valid
• Explain the two valid forms of conditional reasoning
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