The Nature of Mathematics, 12th Edition
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Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Chapter 13
Chapter 14
Chapter 15
Chapter 16
Chapter 17
Chapter 18
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Section 3.4: The Nature of Proof

3.4 Outline

A.  Introduction
     1. theorem
     2. syllogism
B. Direct reasoning
     1. definition
     2. modus ponens
     3. law of detachment
     4. assuming the antecedent
C. Indirect reasoning
     1. definition
     2. modus tollens
     3. denying the consequent
D. Transitive reasoning
     1. definition
     2. formulate a conclusion
E.  Logical proof
F.  Fallacies
     1. fallacy of the converse
     2. fallacy of the inverse
         a. fallacy of the converse
         b. assuming the consequent
         c. counterexample
     3. fallacy of the inverse
         a. fallacy of the antecedent
         b. test validity
     4. false chain pattern

3.4 Essential Ideas

There are three types of syllogisms considered in the text:

These forms can be mixed together in a single problem.
In addition there are three common logical fallacies considered: Remember this forms are NOT valid: