Section 3.4: The Nature of Proof

3.4 Outline

  1. Introduction
    1. theorem
    2. syllogism
  2. Direct reasoning
    1. definition
    2. modus ponens
    3. law of detachment
    4. assuming the antecedent
  3. Indirect reasoning
    1. definition
    2. modus tollens
    3. denying the consequent
  4. Transitive reasoning
    1. definition
    2. formulate a conclusion
  5. Logical proof
  6. Fallacies
    1. fallacy of the converse
      1. also called fallacy
See the whole entry

Section 3.3: Operations and Laws of Logic

3.3 Outline

  1. Biconditional, implication, and logical equivalence
    1. definition of biconditional
    2. verifying tautologies
    3. implication
    4. equivalence
  2. Laws of logic
    1. law of double negation
    2. law of contraposition
    3. De Morgan’s laws
  3. Negation of a compound statement
    1. negation of a conditional
    2. language analysis
  4. Miscellaneous operators
See the whole entry

Section 3.2: Truth Tables and the Conditional

3.2 Outline

  1. Constructing truth tables
    1. fundamental operators (and, or, and not )
    2. truth table
    3. law of double negation
  2. Conditional
    1. translation: if p, then q
    2. antecedent
    3. consequent
    4. uses
    5. definition
  3. Translations for the conditional
    1. converse
    2. inverse
    3. contrapositive
    4. law of
See the whole entry

Section 3.1: Deductive Reasoning

3.1 Outline

  1. Terminology
    1. argument
    2. hypotheses/premises
    3. deductive reasoning
    4. valid
    5. logic
    6. symbolic logic
    7. statement
    8. simple statement
    9. operators (connectives)
    10. compound statement
    11. fuzzy logic
    12. law of the excluded middle
    13. truth value of a simple statement
  2. Conjunction
    1. translation: and
    2. definition
  3. Disjunction
    1. translation: or
    2. definition
  4. Negation
See the whole entry