Types of Tautologies and Argument

• What does the term tautology refer to?

  A compound proposition with all true values
• How is a tautology denoted?

  It is denoted by 𝜏
• What is an example of a tautology?

  p → (p v q)
• Why is p → (p v q) considered a tautology?

  All entries in the last column are true
• What is a contradiction in logic?

  A compound proposition with all false values
• What is an example of a contradiction?

  (p ^ ~q) ^ (p ^ q)
• Why is (p ^ ~q) ^ (p ^ q) considered a contradiction?

  All entries in the last column are false
• What does contingent mean in logic?

  A statement with at least one true and one false
• What is an example of a contingent statement?

  (p → q) ^ (q → p)
• Why is ((p → q) ^ (q → p)) considered contingent?

  It has a combination of true and false values
• What are the types of logical statements discussed?

  • Tautology
  • Contradiction
  • Contingent
• What are the main properties of tautologies?

  1. Associative
  2. Commutative
  3. Distributive
  4. Law of biconditional propositions
  5. Modus Ponens
  6. Modus Tollens
  7. Exportation
  8. Transposition
  9. Addition

  10. Simplification

  11. Conjunction

  12. Double Negation

  13. Absorption

  14. Disjunctive Syllogism

  15. Material Implication

  16. Disjunctive Simplification

  17. Resolution

  18. Hypothetical Syllogism

  19. Constructive Dilemma

  20. Destructive Dilemma
• What is the definition of a valid argument?

  Conclusion is true if premises are true
• What is a fallacy?

  An argument that is not valid
• What is the symbolic form of the argument: "If one has a Pasig Pass QR Code then he is a Pasigueño"?

  P → Q
• How can you check if an argument is valid?

  Rewrite as conditional and construct truth table
• What is the conclusion of the argument about Hubert and the Pasig Pass QR Code?

  Hubert is a Pasigueño
• What does the truth table show for the argument about Hubert?

  It is a tautology
• What is the symbolic representation of "If I’m relaxed, I’m productive"?

  P → Q
• What is the conclusion of the argument about being relaxed and happy?

  If I’m not happy, I’m not relaxed
• What are the steps to determine if an argument is valid or a fallacy?

  1. Translate into symbolic form
  2. Construct a truth table
  3. Analyze the final column
• What is the first example of a valid argument discussed?

  If Tomas was absent, he missed review
• Why is the argument about Tomas valid?

  It follows Modus Ponens reasoning
• What is the second example of an invalid argument discussed?

  I graduated, therefore I passed exam
• Why is the argument about graduation invalid?

  It follows the fallacy of the converse
• What is the third example of an invalid argument discussed?

  He is dumb or lazy
• Why is the argument about being dumb or lazy invalid?

  It misuses Disjunctive Reasoning