Home>Courses>Introduction to Logic: Basics of Mathematical Reasoning

Free

Beginner

Certificate of Completion

Introduction to Logic: Basics of Mathematical Reasoning

Gain insights into formal logic, propositional logic, and first-order logic. Learn about inference rules and master constructing rigorous proofs, enhancing critical thinking and problem-solving skills.

AI-POWERED

Explanations

Adaptive Learning

AI-POWERED

Explanations

Adaptive Learning

This course includes

43 Lessons

6 Assessments

23 Quizzes

Course Overview

What You'll Learn

Course Content

Recommendations

Course Overview

Formal logic provides a systematic and rigorous framework for expressing and analyzing arguments, which enables learners to evaluate the validity of reasoning, fostering critical thinking skills. Proficiency in constructing and understanding proofs enhances problem-solving abilities, encourages precision in thought, and promotes clarity in communication. In this course, you’ll explore propositions and logical connectives in propositional logic. Next, you’ll cover first-order logic, which extends the scope ...Show More

Formal logic provides a systematic and rigorous framework for expressing and analyzing arguments, which enables learners to eval...Show More

What You'll Learn

An understanding of propositional logic

An understanding of first-order logic

An understanding of deductive logic

Familiarity with the structure of mathematical proofs

An understanding of propositional logic

Course Content

Introduction

1 Lessons

Get familiar with the essentials of mathematical logic to enhance reasoning and decision-making.

Background and Motivation

Propositional Logic

3 Lessons

Unpack the core of propositions, logical equivalence, and propositional calculus in mathematical reasoning.

Propositions

Logical Equivalence

Propositional Calculus and Boolean Algebra

Basic Operations

11 Lessons

Work your way through basic logical operations and their properties, including conjunctions, disjunctions, and negations.

Conjunction

Properties of Conjunction

Disjunction

Properties of Disjunction

Negation

Precedence of Operations and Negating Compound Propositions

Logical Equivalence Revisited

Assessment-I

Assessment

Propositional Toolkit

4 Lessons

Break down complex ideas in logical identities, tautologies, contradictory propositions, and fundamental logical operations.

Logical Identities

Tautologies and Contradictions

A Complete Set of Operations

NAND and NOR Operations

Assessment-II

Assessment

Logical Reasoning

9 Lessons

Take a look at logical inference, propositional rules, proofs, common fallacies, and logical puzzles.

Logical Truths and Inference

Inference: Modus Ponens and Modus Tollens

Inference: Addition, Conjunction, and Simplification

Inference: Disjunctive and Hypothetical Syllogism

Inference: Constructive and Destructive Dilemma

Mathematical Proofs: Basics

Mathematical Proofs: A Complex Scenario

Common Mistakes in Arguments

Logical Puzzles

Assessment-III

Assessment

Quantifiers and First Order Logic

5 Lessons

Investigate the use of predicates, quantifiers, variables, and negation in logical reasoning.

Predicates

Universal Quantifiers

Existential Quantifiers

Bounded and Free Variables

Negation of Quantified Statements

Assessment-IV

Assessment

11.

Quantified Logical Reasoning

4 Lessons

Master the steps to nested quantifiers, negation, logical equivalence, and inference rules in reasoning.

Nested Quantifiers

Negation of Nested Quantifiers

Logical Equivalence and Quantifiers

Rules of Inference for Quantified Statements

Assessment-V

Assessment

13.

Proving Theorems

5 Lessons

Break down the methods of proving theorems and strategies to avoid common proof errors.

Direct Proofs

Proof by Contraposition

Proof by Contradiction

Errors and Mistakes in Developing Proofs

Strategies for Proofs

Assessment-VI

Assessment

15.

Conclusion

1 Lessons

Discover the logic behind propositional and first-order logic, enhancing your reasoning skills.

Concluding Remarks

Trusted by 2.6 million developers working at companies

"These are high-quality courses. Trust me. I own around 10 and the price is worth it for the content quality. EducativeInc came at the right time in my career. I'm understanding topics better than with any book or online video tutorial I've done. Truly made for developers. Thanks"

Anthony Walker

@_webarchitect_

"Just finished my first full #ML course: Machine learning for Software Engineers from Educative, Inc. ... Highly recommend!"

Evan Dunbar

ML Engineer

"You guys are the gold standard of crash-courses... Narrow enough that it doesn't need years of study or a full blown book to get the gist, but broad enough that an afternoon of Googling doesn't cut it."

Carlos Matias La Borde

Software Developer

"I spend my days and nights on Educative. It is indispensable. It is such a unique and reader-friendly site"

Souvik Kundu

Front-end Developer

"Your courses are simply awesome, the depth they go into and the breadth of coverage is so good that I don't have to refer to 10 different websites looking for interview topics and content."

Vinay Krishnaiah

Software Developer

"I've tried probably 5-7 different sites and Educative is easily the best. It perfectly blends explanation with interactivity"

Eric Downs

Musician/Entrepeneur

Hands-on Learning Powered by AI

See how Educative uses AI to make your learning more immersive than ever before.

Instant Code Feedback

Evaluate and debug your code with the click of a button. Get real-time feedback on test cases, including time and space complexity of your solutions.

AI-Powered Mock Interviews

Put your skills to the test in a simulated interview setting. Receive personalized feedback based on your performance. Available in Premium & Premium Plus plans.

Adaptive Learning

At various checkpoints throughout Educative courses, you will be prompted to take a quick assessment. Receive a condensed curriculum tailored to your strengths and skill gaps.

Explain with AI

Select any text within any Educative course, and get an instant explanation — without ever leaving your browser.

AI Code Mentor

AI Code Mentor helps you quickly identify errors in your code, learn from your mistakes, and nudge you in the right direction — just like a 1:1 tutor!

Recommended before starting this course

Course

Introduction to Computers & Programming

Gain insights into basic computer anatomy, binary systems, and program lifecycles. Delve into logic building and core programming concepts with hands-on exercises and quizzes to reinforce learning.

beginner

6 hours

Course

Computer Programming for Absolute Beginners

Gain insights into programming fundamentals, history, and language evolution. Learn about code organization, variables, conditional statements, loops, functions, and error handling. Explore how computer programs work.

beginner

39 hours

Course

Introduction to Computers & Programming

beginner

6 hour

Course

Computer Programming for Absolute Beginners

beginner

39 hour

Related Courses and Skill Paths

Course

Mastering Algorithms for Problem Solving in Python

Gain insights into algorithms and their implementation for problem-solving in Python. Learn about recursion, dynamic programming, greedy algorithms, and graph algorithms to enhance coding proficiency and problem-solving skills.

intermediate

28 hours

Course

Beginner to Advanced Computing and Logic Building

Gain insights into fundamental and advanced computational techniques, explore efficient algorithm design, and learn to build interactive games. Discover strategies to tackle FAANG coding challenges.

beginner

46 hours

Course

Theory of Computation

Gain insights into formal languages, regular languages, regular expressions, context-free languages, and Turing machines. Delve into automata models and enhance problem-solving skills through extensive exercises.

beginner

15 hours

Course

Mastering Algorithms for Problem Solving in Python

intermediate

28 hour

Course

Beginner to Advanced Computing and Logic Building

beginner

46 hour

Course

Theory of Computation

beginner

15 hour

Free Resources