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Lemma: The Proving Principle By Contraposition, Contrapositive

The proving principle by contraposition is a valid logical argument. For two propositions $p$ and $q$, it consists of $$\begin{array}{rll} \neg q\Rightarrow \neg p&\text{premise}&\text{e.g. If the roads are not wet, then it is not raining.}\\ \hline p\Rightarrow q&\text{conclusion}&\text{e.g. If it is raining, then the roads are wet.}\\ \end{array} $$

Table of Contents

Proofs: 1

Mentioned in:

Chapters: 1
Definitions: 2
Examples: 3
Explanations: 4
Proofs: 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Propositions: 22 23

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References

Bibliography

1. Mendelson Elliott: "Theory and Problems of Boolean Algebra and Switching Circuits", McGraw-Hill Book Company, 1982
2. Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016