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Chapter: Logical Arguments Used in Mathematical Proofs
In the following, we will introduce some most important types of valid logical arguments. While introducing them, we will also mathematically prove that they are indeed valid. You will learn the techniques of the following types of valid logical arguments:
 deductive reasoning,
 modus ponens,
 modus tollens,
 hypothetical syllogism,
 disjunctive syllogism,
 the proving principle by contradiction,
 the proving principle by contraposition,
 the proving principle by induction.
Feel free to use these techniques, not only when writing mathematical proofs, but also in daily life, e.g. when trying to convince your audience or discussion partners.
Table of Contents
Explanations: 1
 Lemma: A Criterion for Valid Logical Arguments
 Lemma: Modus Ponens
 Lemma: Modus Tollens
 Lemma: Hypothetical Syllogism
 Lemma: Disjunctive Syllogism
 Lemma: The Proving Principle by Contradiction
 Lemma: The Proving Principle By Contraposition, Contrapositive
 Lemma: The Proving Principle by Complete Induction
 Lemma: The Proving Principle by Transfinite Induction
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References
Bibliography
 Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016