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} $$
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```### Table of Contents

Proofs: 1

### Mentioned in:

Chapters: 1

### References

#### Bibliography

**Kane, Jonathan**: "Writing Proofs in Analysis", Springer, 2016

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