Logic Technology Driven by Innovation
Institutions involved: FEU Alabang, FEU Diliman, FEU Tech
Propositions are foundational to logic and mathematics.
Involves technology-driven innovation in logical frameworks.
Mathematical Statements
Fundamental principles used in logic and reasoning.
Definition: Derived from Greek "logos", meaning study or reason.
Nature of Logic:
Science and art of correct thinking.
Systematic body of logical truths governing reasoning.
Formal Study: Systematic study of valid inference and reasoning.
Applied in philosophy, mathematics, semantics, and computer science.
Examines:
Forms of arguments.
Valid forms versus fallacies.
Purpose: Distinguishing good from bad arguments.
Propositions:
Statements that are either true (T) or false (F).
Truth values correspond to binary values: 1 (true), 0 (false).
Characteristics:
Declarative sentences that declare facts.
Cannot be questions, instructions, or opinions.
Examples:
Toronto is the capital of Canada. (Yes)
Read this carefully. (No)
1 + 2 = 3. (Yes)
x + 1 = 2. (No)
What time is it? (No)
Formation:
Generated by combining or negating statements.
Component Statements: Individual statements forming a compound statement.
Connectives: "and", "or", "not", "if...then".
Identify statements, compound statements, or neither:
Diagram connecting components (if...then)
Simple statement examples.
Definition: Refusal or denial of a statement.
Examples:
Statement: The number 9 is odd.
Negation: The number 9 is not odd.
True/False relationship in negation.
Symbolism:
Less than, greater than, less than or equal to, greater than or equal to relations.
Negation Examples for inequalities.
Propositional Variables: Represent propositions (p, q, r).
Truth Values: T, F.
Connectives and their types:
Conjunction (AND, ∧)
Disjunction (OR, ∨)
Negation (NOT, ~ ).
Types of Logical Connectives:
Negation (NOT) ~
Conjunction (AND) ∧
Disjunction (OR) ∨
Exclusive or (XOR) ⊕
Implication (if...then) →
Bi-conditional (if and only if).
Implication: p → q can be read as:
"If p then q"
Various equivalent statements.
Practice in rewriting logical statements from symbols to verbal expressions.
Universal Quantifiers: All, each, no, none.
Existential Quantifiers: Some, there exists.
Patterns of negation in quantified statements.
Importance in logic.
Examples showing true and false statements.
How component statements' truth values determine compound statements.
Example of a conjunction truth table.
Characteristics of Conditionals:
Compound statements using "if...then".
Establishing truth table for conditional statements.
Relationship between conditional statements and their converses/inverses.
Examples demonstrating equivalence.
Exercises on transforming conditional statements into "if...then" form.
Expression of the negation of conditional statements.
Various educational materials and publications supporting the course.
Authors: Barcelona A.B., Oronce O.A., Verzosa D.M.B. et al.
[M5-MAIN] Logic PowerPoint
Logic Technology Driven by Innovation
Institutions involved: FEU Alabang, FEU Diliman, FEU Tech
Propositions are foundational to logic and mathematics.
Involves technology-driven innovation in logical frameworks.
Mathematical Statements
Fundamental principles used in logic and reasoning.
Definition: Derived from Greek "logos", meaning study or reason.
Nature of Logic:
Science and art of correct thinking.
Systematic body of logical truths governing reasoning.
Formal Study: Systematic study of valid inference and reasoning.
Applied in philosophy, mathematics, semantics, and computer science.
Examines:
Forms of arguments.
Valid forms versus fallacies.
Purpose: Distinguishing good from bad arguments.
Propositions:
Statements that are either true (T) or false (F).
Truth values correspond to binary values: 1 (true), 0 (false).
Characteristics:
Declarative sentences that declare facts.
Cannot be questions, instructions, or opinions.
Examples:
Toronto is the capital of Canada. (Yes)
Read this carefully. (No)
1 + 2 = 3. (Yes)
x + 1 = 2. (No)
What time is it? (No)
Formation:
Generated by combining or negating statements.
Component Statements: Individual statements forming a compound statement.
Connectives: "and", "or", "not", "if...then".
Identify statements, compound statements, or neither:
Diagram connecting components (if...then)
Simple statement examples.
Definition: Refusal or denial of a statement.
Examples:
Statement: The number 9 is odd.
Negation: The number 9 is not odd.
True/False relationship in negation.
Symbolism:
Less than, greater than, less than or equal to, greater than or equal to relations.
Negation Examples for inequalities.
Propositional Variables: Represent propositions (p, q, r).
Truth Values: T, F.
Connectives and their types:
Conjunction (AND, ∧)
Disjunction (OR, ∨)
Negation (NOT, ~ ).
Types of Logical Connectives:
Negation (NOT) ~
Conjunction (AND) ∧
Disjunction (OR) ∨
Exclusive or (XOR) ⊕
Implication (if...then) →
Bi-conditional (if and only if). ↔
Implication: p → q can be read as:
"If p then q"
Various equivalent statements.
Practice in rewriting logical statements from symbols to verbal expressions.
Universal Quantifiers: All, each, no, none.
Existential Quantifiers: Some, there exists.
Patterns of negation in quantified statements.
Importance in logic.
Examples showing true and false statements.
How component statements' truth values determine compound statements.
Example of a conjunction truth table.
Characteristics of Conditionals:
Compound statements using "if...then".
Establishing truth table for conditional statements.
Relationship between conditional statements and their converses/inverses.
Examples demonstrating equivalence.
Exercises on transforming conditional statements into "if...then" form.
Expression of the negation of conditional statements.
Various educational materials and publications supporting the course.
Authors: Barcelona A.B., Oronce O.A., Verzosa D.M.B. et al.