About This Chapter
Who's it for?
Anyone who needs help learning or mastering college preparatory math 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 logic and logical fallacies in math.
- Need an efficient way to learn about logic.
- 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 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 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:
- How can I use the language of logic to solve math problems?
- What are logical fallacies?
- What are truth tables and values, and how do I use them?
- How can I differentiate between conjunctions and disjunctions?
- What are conditional statements?
- How can I identify the counterexample, contrapositive, converse and inverse of a logical statement?
1. 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.
2. Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice
Logical fallacies refer to ways people attempt to reason and prove statements that are not based on pure fact. Discover four examples of logical fallacies including hasty generalization, circular reasoning, false cause, and limited choice.
3. Logical Fallacies: Appeals to Ignorance, Emotion or Popularity
Logical fallacies are a means of reasoning which are not based on pure facts. Discover three types of logical fallacies and how to avoid them, including appeal to ignorance, appeal to emotion, and appeal to popularity.
4. 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.
5. Logical Math Connectors: Conjunctions and Disjunctions
Logical math connectors are used to combine two statements with either a conjunction or disjunction. Learn how to recognize statements and discover the importance of connectors and the difference between conjunctions and disjunctions.
6. 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.
7. 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.
8. Law of Contrapositive in Math: Definition & Example
When a statement is reversed and negated, it is the result of a concept known as contrapositive. Discover how to find the contrapositive of conditional statements.
9. What is a Paragraph Proof? - Definition & Examples
Paragraph Proofs are logical arguments presented in factual statements to determine a specific conclusion in a written paragraph. Using provided examples, learn the steps and outline of effective paragraph proofs.
10. Dominant Strategy in Game Theory: Definition & Examples
In game theory, a dominant strategy is a strategy that gives a player the best outcomes, regardless of the actions of the opponent. Understand the definition of dominant strategy and explore examples of situations demonstrating a dominant strategy.
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Other chapters within the College Preparatory Mathematics: Help and Review course
- Math Foundations: Help and Review
- Problem Solving & Reasoning Skills
- Percents in Math Basics
- Decimals & Fractions Overview
- Understanding Fractions & Mixed Numbers
- Linear Equations: Help and Review
- Solving and Graphing Inequalities: Help and Review
- Graphing and Factoring Quadratic Equations: Help and Review
- Complex and Imaginary Numbers: Help and Review
- Properties of Exponents: Help and Review
- Praxis I Math: Square Roots
- Properties of Polynomial Functions: Help and Review
- Simplifying and Solving Rational Expressions: Help and Review
- Praxis I Math: Algebraic Expressions
- Properties of Functions: Help and Review
- Logarithms and Exponential Equations: Help and Review
- Data & Estimation
- Sets: Help and Review
- Basic Probability and Statistics: Help and Review
- Praxis I Math: Basic Statistics and Probability
- Geometric Laws & Proofs
- Grade Level Math Vocabulary: Help and Review
- MTEL Middle School Math/Science: History of Geometry
- MTEL Middle School Math/Science: Geometric Properties & Theorems
- MTEL Middle School Math/Science: Principles of Geometry
- MTEL Middle School Math/Science: Algebraic Applications in Geometry
- MTEL Middle School Math/Science: Using Trigonometric Functions
- MTEL Middle School Math/Science: Trigonometric Identities
- MTEL Middle School Math/Science: Trigonometric Applications
- Praxis I Math: Ratio and Proportions
- Praxis I Math: Congruence and Similarity
- Praxis I Math: Geometric Measurement and Dimension