# Ch 36: Using Logic in Math

### About This Chapter

## Using Logic in Math - Chapter Summary

Our instructors explain some of the ways that logic is used in math in this informative chapter. These short and interesting lessons cover truth values, truth tables and propositions, as well as conditional statements as they're used in math. You'll also review logic laws and how both inductive and deductive reasoning are utilized in mathematics. After completing this chapter, you should be able to:

- Use mathematical models to solve problems
- Describe the mathematical principles used in problem solving
- Identify the three-way principle of mathematics
- Understand the concept of estimation in math
- Explain how logic and critical thinking are used in math

These mobile-friendly and easy-to-use learning tools make it possible to study any time that works best for you. The short video lessons are followed by multiple-choice quizzes to test your comprehension and readiness for test day. If you prefer to work offline, the printable lesson transcripts in this chapter make great study guides. If at any time you need help, our professional instructors are available to offer assistance.

### 1. Propositions, Truth Values and Truth Tables

A proposition is a statement that can be given one of two truth values: it's either true or it is false. Explore how truth values can be placed into a truth table using one of four logic combinations.

### 2. Conditional Statements in Math

A conditional statement is a type of mathematical logic that uses an if-then structure to combine two statements; however, conditional statements may not make sense in reality. Investigate the parts of a conditional statement, and discover how a statement can be true in the world of logic, but false in the real world.

### 3. Logic Laws: Converse, Inverse, Contrapositive & Counterexample

The validity of a logical statement often can be determined by looking at its logical equivalence. Learn about the logical variants of a conditional statement, and explore the definitions of converse, inverse, contrapositive, and counterexample.

### 4. Reasoning in Mathematics: Inductive and Deductive Reasoning

Inductive and deductive reasoning are two methods of reasoning used in mathematics. Explore the definitions of inductive and deductive reasoning, review examples of each in action, and learn when and how to use them.

### 5. Mathematical Principles for Problem Solving

Solving problems, both in math and in life, involves five mathematical principles: always, counterexample, order, splitting hairs, and analogies. Delve into the definition of each principle and learn when and how to use them.

### 6. The Three-Way Principle of Mathematics

The three-way principle of mathematics states that there are three ways to solve a math problem: verbally, graphically, or by example. Learn how to use these methods and explore the strengths and limitations of each.

### 7. How to Estimate in Math: Definition & Concept

Estimating is the use of approximation to arrive at a conclusion similar to the correct answer. Learn the general rule as well as applications of decimals and rounding in estimation in various places.

### 8. Using Mathematical Models to Solve Problems

Mathematical models are used to represent word problems in equations which can help solve the problem. Learn about an introduction to mathematical modeling, and understand why a mathematical model is not a completely accurate representation of the real world.

### 9. Critical Thinking and Logic in Mathematics

Mathematics involves logic and critical thinking to make connections and draw conclusions. Explore how to use logic, propositions, true or false, and critical thinking in math problems.

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### Other Chapters

Other chapters within the AEPA Essential Academic Skills: Practice & Study Guide course

- Sentence Types & Their Structures
- Grammar Conventions in Writing
- Basic Writing Mechanics
- Word Meanings & Figurative Language
- Word & Sentence Choice
- Components of an Essay
- Developing & Organizing Essays
- Identifying Errors in Writing
- Developing Reading Comprehension Skills
- Identifying the Main Idea & Purpose of Written Works
- Analyzing, Interpreting & Evaluating Reasoning
- Organizing Information Using Written & Graphic Forms
- Basic Number Structure
- Basic Number Operations
- Overview of Math Properties
- Concept of Equality in Math
- Understanding Operations with Fractions
- Understanding Operations with Decimals
- Understanding Operations with Percents
- Overview of Ratios, Proportions & Rate of Change
- Understanding Exponents & Scientific Notation
- Principles of Algebra
- Methods for Solving Algebraic Equations
- Understanding & Solving Linear Equations
- Graphing Points, Lines & Functions
- Understanding the Properties of Functions
- Rules of Measurements
- Principles of Geometry
- Understanding Geometric Shapes & Their Properties
- Overview of Area, Perimeter, Surface Area & Volume
- Pythagorean Theorem & Right Triangles
- Using Different Types of Data
- Visual Depictions of Data
- Summarizing Data Sets
- Probability & Statistics Basics
- Methods for Solving Math Word Problems
- AEPA Essential Academic Skills Flashcards