About This Chapter
MTLE Basic Skills: Using Logic to Solve Problems - Chapter Summary
The interactive lessons in this chapter are effective at helping you review logic-related principles and material for the MTLE Basic Skills exam. These include:
- Logic and critical thinking
- Different types of logical fallacies
- Truth values, truth tables and propositions
- Logical math connectors
- Conditional statements
- Logical equivalence
- Inductive vs. deductive reasoning
- Direct proofs
- The proof by contradiction method
In order to develop your logic skills for the exam, go through each lesson in this chapter. They were made to help you become comfortable with the kinds of logic problems that will be on the exam. There are video tags in each lesson, which allow you to scroll through different parts. You also have access to online instructors who will help resolve any confusion you might have about topics discussed in this chapter.
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. 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.
4. 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.
5. 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.
6. 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.
7. The Differences Between Inductive and Deductive Reasoning
Inductive and deductive reasoning are often confused. This lesson introduces the concept of reasoning and gives you tips and tricks to keeping inductive and deductive reasoning straight.
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.
9. Proof by Contradiction: Definition & Examples
One of several different ways to prove a statement in mathematics is proof by contradiction. Learn the definition of this method and observe how it is applied to proving a statement's truth value through examples and exploration.
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Other chapters within the MTLE Basic Skills: Practice & Study Guide course
- MTLE Basic Skills: Determining Word Meanings
- MTLE Basic Skills: Figurative Language
- MTLE Basic Skills: Increasing Vocabulary
- MTLE Basic Skills: Main Idea in Literature
- MTLE Basic Skills: Literary Purpose & Audience
- MTLE Basic Skills: Word Choice in Literature
- MTLE Basic Skills: Relationships Between Ideas in Writing
- MTLE Basic Skills: Analyzing Written Material
- MTLE Basic Skills: Summarizing & Interpreting Information
- MTLE Basic Skills: Presenting Ideas in Writing
- MTLE Basic Skills: Writing Mechanics
- MTLE Basic Skills: Spelling & Punctuation
- MTLE Basic Skills: Writing for Intent & Audience
- MTLE Basic Skills: Numbers
- MTLE Basic Skills: Operations With Integers
- MTLE Basic Skills: Fractions
- MTLE Basic Skills: Decimals
- MTLE Basic Skills: Percentages
- MTLE Basic Skills: Exponents
- MTLE Basic Skills: Solving Math Problems
- MTLE Basic Skills: Algebraic Patterns & Expressions
- MTLE Basic Skills: Equations, Functions & Factoring
- MTLE Basic Skills: Linear & Nonlinear Functions
- MTLE Basic Skills: Measurement, Units & Operations
- MTLE Basic Skills: Measurement, Shapes & Angles
- MTLE Basic Skills: Calculating Measurements Indirectly
- MTLE Basic Skills: Solving Measurement Problems
- MTLE Basic Skills: Principles of Geometry
- MTLE Basic Skills: Using Geometry to Solve Problems
- MTLE Basic Skills: Statistics & Discrete Mathematics
- MTLE Basic Skills: Probability
- MTLE Basic Skills: Applications of Discrete Mathematics
- MTLE Basic Skills: Problem Solving Strategies
- MTLE Basic Skills: Mathematical Language & Connections
- MTLE Basic Skills Flashcards