Denying the Antecedent

What is Denying the Antecedent?

If P, then Q. Not P. Therefore, not Q.

Even if P doesn’t happen, Q could still be true for other reasons.

Example

If the country is corrupted, people will lose faith in the government.

The people did not lose faith in the government.

Therefore, the country is not corrupted.

Even if the people did not lose faith in the government, the country could still be corrupted.