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
$$\begin{array}{rll}
p\Rightarrow q&\text{major premise}&\text{e.g. If a number$n\neq 2$is a prime number, then it is odd.}\\
q&\text{minor premise}&\text{e.g. The number$n$is odd.}\\
\hline
p&\text{conclusion}&\text{e.g. Therefore,$n\neq 2$and$n$is a prime number.}\\
\end{array} $$
Proofs: 1
Chapters: 1
