Introduction to Logical Reasoning - Mathematics (Senior Secondary)

This course provides a formal introduction to the principles of mathematical logic. It moves beyond simple calculation to focus on the structure and validity of mathematical statements. You will learn to identify and analyse simple and compound statements, understand the concept of truth values, and use symbolic logic to represent arguments. Logical reasoning is the bedrock of mathematics and computer science. While other topics teach you how to calculate, this subject teaches you how to think and construct valid arguments. This skill is non-negotiable for writing proofs, developing algorithms, and designing complex systems where precision and the absence of ambiguity are critical. By the end of this course, you will be able to define a mathematical statement and determine its truth value. You will understand and use logical operators such as conjunction and conditional statements. You will also be able to translate simple verbal arguments into symbolic logic. This course is designed for students who are beginning to engage with more abstract mathematical concepts. It is essential for anyone intending to study higher mathematics, computer science, or philosophy. No prior knowledge is required beyond a clear thought process.

Enrolment valid for 12 months

Course Chapters

1. Introduction

This chapter introduces the field of mathematical logic. It defines its purpose and explains why a formal system of reasoning is essential in mathematics and other technical fields. Key learning objectives include defining logical reasoning and appreciating its role in ensuring mathematical precision.

Chapter lessons

1-1. Welcome

This lesson outlines the course structure and goals. It defines logical reasoning and explains how this course teaches the method of thinking with mathematical precision.

2. Simple and Compound Statements

This chapter focuses on the building blocks of logic. It defines a valid statement, introduces the concept of its truth value, and explores how simple statements are combined using logical operators. Key learning objectives include identifying simple and compound statements and determining the truth value of a statement and its negation.

Chapter lessons

2-1. Meaning of a simple statement

This lesson defines the criteria for a simple mathematical statement and distinguishes it from questions, commands, or opinions.

2-2. Truth value and negation of simple statements

This lesson introduces the concept of a truth value (true or false). It also covers how to correctly form the negation of a statement.

2-3. Compound statements and logical operators

This lesson explains how simple statements are joined by logical operators (like AND, OR, IF...THEN) to form compound statements and introduces their symbols.

3. Truth Tables

This chapter introduces truth tables as a systematic tool for evaluating the truth value of complex compound statements under all possible scenarios. Key learning objectives include constructing a truth table for any given compound statement involving two variables and identifying tautologies and contradictions.

Chapter lessons

3-1. Constructing truth tables

This lesson provides a step-by-step guide on how to set up and fill in a truth table for conjunction (AND), disjunction (OR), and negation (NOT).

3-2. Truth tables for conditional statements

This lesson focuses specifically on constructing truth tables for conditional (IF...THEN) and biconditional (IF AND ONLY IF) statements.

4. Conclusion and Next Steps

This final chapter summarises the foundational concepts of logical reasoning, reinforcing the understanding of statements, operators, and truth tables. Key outcomes include a review of the principles of mathematical logic and an understanding of the importance of this skill for further studies.

Chapter lessons

4-1. Summary of what you have learned

This lesson provides a concise review of the course content, recapping simple and compound statements, truth values, logical operators, and the use of truth tables.

4-2. The importance of logic in mathematics and beyond

This lesson places the acquired knowledge in a broader context. It explains how logical reasoning is the foundation for writing mathematical proofs, programming, and constructing valid arguments in any field, from law to business.