Objective 6

 Distinguishing Propositional Logic and Predicate Logic in Determining the Validity of a Given Proposition

Introduction to Basic Connectives:

• Negation:

  • Involves reversing the truth value of a proposition.
  • Symbolized by ¬ (not).

• Disjunction:

  • Represents the "or" relationship between two propositions.
  • Symbolized by ∨ (or).

• Conjunction:

• Represents the "and" relationship between two propositions.
• Symbolized by ∧ (and).

Morgan's Laws:

• Laws of Morgan:
• Describes the relationship between negation, conjunction, and disjunction.
• ¬(p ∧ q) ≡ (¬p ∨ ¬q) (Negation of a Conjunction)
• ¬(p ∨ q) ≡ (¬p ∧ ¬q) (Negation of a Disjunction)

Conditional Propositions and Logical Equivalences:

• Conditional Propositions:
• Represented by "if-then" statements.
• Symbolized by → (implies).
• Equivalences such as Modus Ponens and Modus Tollens.

Reasoning and Demonstrations:

• Rational and Logical Reasoning:
• Use of connectives to form valid arguments.
• Demonstrations of logical principles and deductions.

Truth Tables:

• Truth Tables:
• A systematic way to represent the possible truth values of propositions.
• Helps in determining the truth value of compound propositions.

Tautology, Contradictions, and Contingencies:

Tautology:

• A compound proposition that is always true.
• Example: p ∨ ¬p.

Contradiction:

• A compound proposition that is always false.
• Example: p ∧ ¬p.

Contingency:

• A compound proposition that is neither a tautology nor a contradiction.
• Its truth value depends on the truth values of its components.