Denying the antecedent
Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement. It is committed by reasoning in the form:
If P, then Q.
Therefore, if not P, then not Q.which may also be phrased as

    P
    →
    Q
  

{\displaystyle P\rightarrow Q}
  (P implies Q)



  
    ∴
    ¬
    P
    →
    ¬
    Q
  

{\displaystyle \therefore \neg P\rightarrow \neg Q}
  (therefore, not-P implies not-Q)Arguments of this form are invalid. Informally, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true.

The name denying the antecedent derives from the premise "not P", which denies the "if" clause of the conditional premise.