About This Chapter
Logic & Algebra - Chapter Summary
Our instructors have developed fun lessons you can access anytime to study logic and algebra. This chapter provides in-depth analyses of topics that include tautology in math, the algebra of sets and the Karnaugh map. Once you've completed the lessons, you will be ready to do the following:
- Discuss the format of algebraic proofs
- Detail the role and provide examples of propositional logic in algebra
- Exhibit knowledge of propositions, truth values and truth tables
- Identify conjunctions and disjunctions and discuss connectors used with each
- Define tautology in math and the algebra of sets
- Explain the rules, theorems and properties of Boolean algebra
- Share details about Boolean logic, operators and expressions
- Provide the definition and examples of the Karnaugh map
Absorb information about logic and algebra your way by accessing any number of lessons in this chapter in your sequence of choice. If you develop questions during your review of the lessons, feel free to submit them to our experts. When ready, check your understanding of each lesson by taking its accompanying quiz. A practice exam is available to test your knowledge of the entire chapter.
1. Algebraic Proofs: Format & Examples
Algebraic proofs are actually kind of cool. Watch this video lesson to see how an algebraic proof shows you the mathematical reasoning behind your algebraic solutions. Use this method to show your teachers why your answer is the right one.
2. 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.
3. 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.
4. 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.
5. The Algebra of Sets: Properties & Laws of Set Theory
The algebra of sets is an analysis of values. This lesson provides an overview of the properties of sets and laws of set theory and illustrates them with real-life examples.
6. Boolean Algebra: Rules, Theorems, Properties & Examples
In this lesson you will discover and use the rules of Boolean algebra to simplify Boolean expressions (statements that are either True or False). The Rules of Boolean algebra are given in a table, and a few examples show how to use them.
7. Boolean Logic, Operators & Expressions
Programming uses Booleans, which are used to represent values of true and false. Many operations use Boolean logic. Learn how Boolean operators and expressions are used.
8. What is a Karnaugh Map? - Definition & Examples
In this lesson, you'll learn how a Karnaugh map can help you map out results from a Boolean expression. This is especially useful when working with electronic circuits that work off of Boolean logic.
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Other chapters within the VCE Specialist Mathematics: Exam Prep & Study Guide course
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- Sequences & Series
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- Graphing Linear & Non-Linear Relations
- Understanding & Graphing Functions
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- Categorical Data Representation
- Numerical Data Representation
- Sampling & Distribution in Statistics
- Probability & Statistics Overview
- Principles of Counting
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- Applications of Integrals
- Differential Equations in Calculus
- Vectors & Vector Calculus
- Understanding Kinematics
- Understanding Mechanics
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