Denying the Antecedent  Examples & Definition
Denying the antecedent is the error of assuming that if the initial condition (P) is not met, the expected result (Q) won’t occur either.
This logical fallacy is expressed as follows:
 If P, then Q.
 Not P.
 Therefore, not Q.
The logical fallacy of denying the antecedent is typically found in domains that involve formal logical reasoning, such as math, science, and law.
What is denying the antecedent?
Denying the antecedent occurs when someone mistakenly concludes that if the initial condition (P) of a situation isn’t fulfilled, then the expected outcome (Q) can’t occur either.
It is a formal logical fallacy that occurs in deductive reasoning using hypothetical syllogisms. The fallacy is defined by the following formula:
 If P, then Q.
 Not P.
 Therefore, not Q.
This logical structure is recognized as invalid because the truth of Q is not solely dependent on the condition P being true. Other conditions could still make Q true. Thus, the conclusion does not follow logically from the premises.
Denying the antecedent examples
Examples of the denying the antecedent fallacy are often found in contexts such as math, where deductive reasoning is essential.
They are also commonly found in scientific contexts.
Denying the antecedent vs modus tollens
The valid way to negate hypothetical syllogisms is called modus tollens (or “denying the consequent”). It involves proving that an initial condition (P) didn’t happen because a necessary consequence (Q) didn’t happen. It takes the following form:
Modus tollens (valid):
 If P, then Q.
 Not Q.
 Therefore, not P.
In contrast, denying the antecedent involves making the mistake of erroneously trying to prove that an effect didn’t happen just because one possible (but nonexclusive) cause didn’t happen.
Denying the antecedent (invalid):
 If P, then Q.
 Not P.
 Therefore, not Q.
Frequently asked questions about denying the antecedent
 Why is denying the antecedent a fallacy?

Denying the antecedent is a logical fallacy because the absence of one potential cause doesn’t mean that no other causes exist.
Consider the following example:
 If it’s raining (antecedent), then the ground is wet (consequent).
 It’s not raining.
 Therefore, the ground is not wet.
This argument is clearly faulty because the ground could be wet for many reasons other than rain (e.g., lawn sprinklers). In other words, the conclusion is not solely dependent on the premise.
 Is denying the antecedent valid or invalid?

Denying the antecedent is an invalid argument form. In other words, it is a formal logical fallacy.
In logic, the term “invalid” describes a type of argument in which the premises do not guarantee the truth of the conclusion, even if all the premises are true. In the fallacy of denying the antecedent, it is possible that the expected outcome could occur without one specific cause being true.
Consider the following example:
 If an animal is a bird, then it lays eggs.
 This animal is not a bird.
 Therefore, it does not lay eggs.
It is clear that this argument is invalid. The animal could be an insect or a reptile or many other animals. The conclusion is not guaranteed by the premises.
 What is a reallife example of denying the antecedent?

A reallife example of denying the antecedent is the following argument:
 If someone is a professor, then they have a PhD.
 Maria is not a professor.
 Therefore, Maria does not have a PhD.
This is an invalid argument because the fact that Maria is not a professor does not necessarily mean she does not have a PhD. Maria might be someone who has a PhD but chose a nonacademic career path.