### 3.4 Fallacies in Logic

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• Math Help

In logic, the premise

If P, then Q

Premise

is logically equivalent to its contrapositive

If not Q, then not P.

Contrapositive

The contrapositive, however, is not what is involved in denying the antecedent.

 • Premise: When it rains, the ground gets wet. If P, then Q. • Premise: It isn't raining. Not P. • Conclusion: Therefore, the ground is not wet. Therefore, not Q.

Do you see why the type of fallacy is called denying the antecedent?

• Consumer Suggestion

A “lemon” is referred to as a new car that repeatedly fails to meet standards of quality and performance. “Lemon law” is the common name for the laws that help consumers if a new car fails and the manufacturer does not honor the warranty.

Visit Lemon Law America to see the lemon laws for your state. You can also see a new car guide for buying tips if you are looking to purchase a new car.

• Checkpoint Solution

Here is the original statement.

The buyer of a new vehicle brought claims against a manufacturer under Ohio's Lemon Law and for breaches of a warranty act. The trial court ruled in favor of the defendant on both claims. The court of appeals analyzed the trial court's logic. The trial court first addressed the plaintiff's Lemon Law claim and determined that it was invalid. Next, the trial court concluded that since the Lemon Law claim was not valid, the warranty act claim was not valid. The court of appeals rejected the trial court's reasoning, based on the fallacy of denying the antecedent.

Summarized from "Conventional Logic: Using the Logical Fallacy of Denying the Antecedent as a Litigation Tool," Stephen Rice

Here is a possible rewriting as a syllogism.

 • Premise: If the Lemon Law claim is valid, then the automobile warranty is valid. • Premise: The Lemon Law claim is not valid. • Conclusion: Therefore, the automobile warranty is not valid.

In this form, you can see that the syllogism is a fallacy and that it is of the form denying the antecedent.

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