1. Introduction to Mathematical Logic - Discrete Mathematics - Vol 1
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

1. Introduction to Mathematical Logic

1. Introduction to Mathematical Logic

Mathematical logic is a crucial field that addresses the science of reasoning and verification of statements. It encompasses propositional logic, which serves as the foundation for various logical operators such as conjunction, disjunction, and negation. The study of logical implications and their interpretations is vital in numerous applications including program verification and artificial intelligence.

13 sections

Enroll to start learning

You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

Navigate through the learning materials and practice exercises.

  1. 1
    Introduction To Mathematical Logic

    Mathematical logic is the science of reasoning, focusing on verifying the...

  2. 1.1
    What Is Mathematical Logic?

    Mathematical logic is the science of reasoning, focusing on validating...

  3. 1.2
    Applications Of Mathematical Logic

    Mathematical logic is the study of reasoning, which has significant...

  4. 1.3
    Types Of Mathematical Logic

    This section introduces the types of mathematical logic, focusing on...

  5. 1.4
    Propositional Logic

    This section introduces propositional logic, discussing its definition,...

  6. 1.4.1
    Definition Of Proposition

    This section defines propositional logic and introduces the concept of...

  7. 1.4.2
    Propositional Variables

    This section introduces propositional variables, defining them as...

  8. 1.4.3
    Compound Propositions

    This section introduces compound propositions, utilizing logical operators...

  9. 1.4.3.1
    Logical Operators

    This section introduces logical operators, defined as constructs that...

  10. 1.4.3.2
    Number Of Distinct Logical Operators

    This section explains the concept of logical operators within mathematical...

  11. 1.4.4
    Conditional Statements

    This section introduces conditional statements in mathematical logic,...

  12. 1.4.4.1
    Interpretations Of Conditional Statements

    This section focuses on the various interpretations of conditional...

  13. 1.5

    The conclusion summarizes the importance and applications of mathematical...

What we have learnt

  • Mathematical logic helps in determining the truth or falsehood of mathematical statements.
  • Propositional logic consists of declarative statements that can be classified as true or false, and various logical operators can be utilized to combine these statements.
  • There are distinct logical operators used within mathematical logic, including AND (conjunction), OR (disjunction), and implications, each with its unique applications and truth tables.

Key Concepts

-- Proposition
A declarative statement that can be either true or false, but not both simultaneously.
-- Logical Operators
Symbols like OR, AND, and NOT that perform operations on propositions to yield a resulting truth value.
-- Implication
A conditional statement that describes the relationship where one proposition (p) leads to another (q), symbolized as p → q.
-- Truth Table
A table that lists all possible truth values for a set of propositions and the corresponding result of the logical operations.

Additional Learning Materials

Supplementary resources to enhance your learning experience.