Lemma: Mixing-up the Sufficient and Necessary Conditions

Another common fallacy is mixing up the sufficient and necessary conditions of an implication "$\Rightarrow$". Given two propositions $p$ and $q$, this fallacy takes the following form:

$$\begin{array}{rll} p\Rightarrow q&\text{premise}&\text{e.g. Any square is a rectangle.}\\ \hline q\Rightarrow p&\text{conclusion}&\text{e.g. Therefore, any rectangle is a square.}\\ \end{array} $$

Proofs: 1

Chapters: 1
Lemmas: 2
Proofs: 3 4 5


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References

Bibliography

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