About This Chapter
Is your logic impeccable? Well, what are the premises of your argument, and how did you reach your conclusion? Our logic lessons will cause you to question your questions, your answers and the steps in between. As we exercise our critical thinking skills, we'll also learn how to avoid pitfalls, intuitive traps that stretch logic. You'll investigate the different forms a logical fallacy can take, such as hasty generalization, circular reasoning, false cause and limited choice. You may be surprised by how often these logical shortcomings come up in everyday life.
Logic is a structured search for truth that takes on many shapes and styles. You'll study how logic looks past appeals to emotion, popularity and ignorance. Our search for truth will lead us to propositions as well as to the truth tables and truth values that follow. If a proposition is false, then is its negation true? You'll learn this and more as we continue our logical journey.
Mathematics has its own language, and logic pays particularly close attention to phrasing. You'll achieve fluency in the language of logic when we give the lowdown on conjunctions, disjunctions and other logical connectives. We'll also explore conditional statements, the phrasing that makes up propositions, hypotheses and conclusions. Truth can take on many forms, so we'll also look at logical equivalence. Our last lesson will cover inverses, converses, contrapositives and counterexamples to show how mathematical statements can be restructured. Along the way, there will be plenty of real-world examples to help the concepts stick. Taking advantage of this great opportunity is the only logical conclusion!
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 Math 102: College Mathematics course
- Math Foundations
- Linear Equations
- Solving and Graphing Inequalities
- Graphing and Factoring Quadratic Equations
- Complex and Imaginary Numbers
- Properties of Exponents
- Properties of Polynomials
- Simplifying and Solving Rational Expressions
- Properties of Functions
- Logarithms and Exponential Equations
- Probability and Statistics
- Studying for Math 102