Lemma: Denying the Antecedent of an Implication

Another example of a fallacy is denying the antecedent of an implication. For two propositions $p$ and $q$, this fallacy takes the following form:

$$\begin{array}{rll} p\Rightarrow q&\text{major premise}&\text{e.g. If you learn maths, then you'll get a good job.}\\ \neg p&\text{minor premise}&\text{e.g. You don't learn maths.}\\ \hline \neg q&\text{conclusion}&\text{e.g. Therefore, you won't get a good job.}\\ \end{array} $$

Here comes another example:

$$\begin{array}{rll} p\Rightarrow q&\text{major premise}&\text{e.g. If two lines are parallel, then they are in the same plane.}\\ \neg p&\text{minor premise}&\text{e.g. The lines are not parallel.}\\ \hline \neg q&\text{conclusion}&\text{e.g. Therefore, they are not in the same plane.}\\ \end{array} $$

Proofs: 1

Chapters: 1

Thank you to the contributors under CC BY-SA 4.0!




  1. Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016