Ch 2: Logic in Mathematics: Help and Review

About This Chapter

The Logic in Mathematics chapter of this High School Geometry Help and Review course is the simplest way to master mathematical logic. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure students learn the essentials of logic in mathematics.

Who's it for?

Anyone who needs help understanding high school geometry material will benefit from taking this course. You will be able to grasp the subject matter faster, retain critical knowledge longer and earn better grades. You're in the right place if you:

  • Have fallen behind in understanding the role of mathematical logic in geometry.
  • Need an efficient way to learn about logic in mathematics.
  • Learn best with engaging auditory and visual tools.
  • Struggle with learning disabilities or learning differences, including autism and ADHD.
  • Experience difficulty understanding your teachers.
  • Missed class time and need to catch up.
  • Can't access extra math learning resources at school.

How it works:

  • Start at the beginning, or identify the topics that you need help with.
  • Watch and learn from fun videos, reviewing as needed.
  • Refer to the video transcripts to reinforce your learning.
  • Test your understanding of each lesson with short quizzes.
  • Submit questions to one of our instructors for personalized support if you need extra help.
  • Verify you're ready by completing the Logic in Mathematics chapter exam.

Why it works:

  • Study Efficiently: Skip what you know, review what you don't.
  • Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
  • Be Ready on Test Day: Use the Logic in Mathematics chapter exam to be prepared.
  • Get Extra Support: Ask our subject-matter experts any relevant question. They're here to help!
  • Study With Flexibility: Watch videos on any web-ready device.

Students will review:

In this chapter, you'll learn the answers to questions including:

  • What roles do critical thinking and logic play in mathematics?
  • What are the four types of logical fallacies, and how can they be avoided?
  • How do appeals to emotion, ignorance or popularity lead to logical fallacies?
  • What is a proposition, and how can it influence a truth value?
  • How do conjunctions and disjunctions in math differ?
  • What is the definition of a conditional statement?
  • How do direct proofs work?
  • What steps are involved in using a geometric proof?

13 Lessons in Chapter 2: Logic in Mathematics: Help and Review
Test your knowledge with a 30-question chapter practice test
Critical Thinking and Logic in Mathematics

1. Critical Thinking and Logic in Mathematics

Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.

Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

2. Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

Watch this video lesson to see how you can identify cases where logic is not sound. Learn the characteristic traits of hasty generalization, circular reasoning, false cause, and limited choice.

Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

3. Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

Watch this video lesson to see examples of the logical fallacies of appeals to ignorance, emotion, and popularity. You will also see how to identify them.

Propositions, Truth Values and Truth Tables

4. Propositions, Truth Values and Truth Tables

Watch this video lesson and learn what truth values are and what a truth table looks like. Learn how to go from a proposition to its negation and how that affects the truth values and the truth tables.

Logical Math Connectors: Conjunctions and Disjunctions

5. Logical Math Connectors: Conjunctions and Disjunctions

Watch this video lesson to learn how to identify conjunctions and disjunctions. Also learn the connectors that are used with each. Learn how you can use them to make statements.

Conditional Statements in Math

6. Conditional Statements in Math

Sometimes, what is true in the mathematical world of logic is false in the real world. Check out this lesson to learn how to identify conditional statements and how you can differentiate between what is logically true and what is true in reality.

Logic Laws: Converse, Inverse, Contrapositive & Counterexample

7. Logic Laws: Converse, Inverse, Contrapositive & Counterexample

Logical statements can be useful, but only if we are able to determine their validity. In this lesson, we'll look at the various forms of a logical statement and see how they relate to each other.

Direct Proofs: Definition and Applications

8. Direct Proofs: Definition and Applications

In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.

Geometric Proofs: Definition and Format

9. Geometric Proofs: Definition and Format

Do you have something to prove? Can you explain why? In this lesson, we'll learn all about geometric proofs, including the parts that comprise a proof.

Basis Point: Definition, Value & Conversion

10. Basis Point: Definition, Value & Conversion

In this lesson, you will learn the definition and value of a basis point. You will also learn how to convert a basis point to a percentage and vice versa. Following this lesson will be a brief quiz to test your new knowledge.

Tautology in Math: Definition & Examples

11. Tautology in Math: Definition & Examples

Discover what a tautology is, and learn how to determine if a statement is a tautology by constructing a truth table. Test your skills with a short quiz.

Antisymmetric Relation: Definition, Proof & Examples

12. Antisymmetric Relation: Definition, Proof & Examples

This lesson will talk about a certain type of relation called an antisymmetric relation. We will look at the properties of these relations, examples, and how to prove that a relation is antisymmetric.

Difference Between Asymmetric & Antisymmetric Relation

13. Difference Between Asymmetric & Antisymmetric Relation

We will explore relations that are antisymmetric and asymmetric in both a real-world context and a mathematical context. We will examine properties of each of these types of relations, and determine how best to tell them apart by their differences.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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