# Lemma: Affirming the Consequent of an Implication

Similar to mixing-up the necessary and sufficient condition of an implication is a fallacy known as the affirming the consequent. It is often used to manipulate the opinion of the audience about a proposed action. Given two propositions $p$ and $q$, it takes the following form:

$$\begin{array}{rll} p\Rightarrow q&\text{major premise}&\text{e.g. If we want to succeed, then we have to take the risk.}\\ q&\text{minor premise}&\text{e.g. I tell you, we have to take the risk.}\\ \hline p&\text{conclusion}&\text{e.g. Therefore, we will succeed.}\\ \end{array}$$

Another, more mathematical example of this fallacy is

$$\begin{array}{rll} p\Rightarrow q&\text{major premise}&\text{e.g. If a numbern\neq 2is a prime number, then it is odd.}\\ q&\text{minor premise}&\text{e.g. The numbernis odd.}\\ \hline p&\text{conclusion}&\text{e.g. Therefore,n\neq 2andnis a prime number.}\\ \end{array}$$

 Table of Contents Proofs: 1 Mentioned in: Chapters: 1 Thank you to the contributors under CC BY-SA 4.0! Github: References Bibliography Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016 
 Feeds Acknowledgments Terms of Use Privacy Policy Disclaimer © 2014+ Powered by bookofproofs, All rights reserved.