About This Chapter
Basic Mathematical Logic - Chapter Summary
This comprehensive overview of basic mathematical logic simplifies the process of understanding logical fallacies, conditional statements in math, logical math connectors and much more. Examine the basics of critical thinking, and grasp aspects of logical equivalence. Upon completion of this chapter, you will be ready to:
- Define critical thinking and logic as they relate to mathematics
- Discuss hasty generalizations, circular reasoning, appeals to ignorance and other logical fallacies
- Exhibit an understanding of propositions, truth values and truth tables
- Describe logical math connectors, including conjunctions and disjunctions
- Explain the meaning of conditional statements in math
- Demonstrate knowledge of logical equivalence
Access the lessons in this chapter as short videos or full transcripts, based on your preferred method of study. Take advantage of clickable timelines located below the videos that enable you to jump to primary topics without watching the lessons in their entirety. If you hit a snag or need additional details about lesson topics, feel free to send your questions to our experts. At any time, test your understanding of basic mathematical logic using lesson quizzes and a chapter exam.
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.
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.
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.
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.
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.
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.
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.
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Other chapters within the CAHSEE Math Exam: Test Prep & Study Guide course
- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Algebraic Linear Equations & Inequalities
- Problems with Exponents
- Overview of Functions
- Rational Expressions & Practice
- Calculations with Ratios, Percent & Proportions
- Understanding Matrices & Absolute Value
- Quadratics & Polynomials
- Geometry: Graphing Basics
- Graphing on the Coordinate Plane
- Measurement in Math
- Properties of Shapes
- Triangles, the Pythagorean Theorem & Congruency
- Perimeter, Area & Volume in Geometry
- Statistics, Probability & Working with Data
- Mathematical Reasoning
- CAHSEE Math Exam Flashcards