About This Chapter
Understanding Sets - Chapter Summary
Get the comprehensive overview of sets you need with help from the short video lessons in this chapter. Expert instructors provide in-depth analyses of Venn diagrams, categorical propositions, two-way tables and other related concepts. Review the lessons at your own leisure. When finished, you will be ready to:
- Define and discuss mathematical sets
- Share the meaning of cardinality and list types of subsets
- Find the Cartesian product
- Discuss the basics of Venn diagrams
- Describe categorical propositions
- Change categorical propositions to standard form
- Provide the definition of a two-way table
Select the lessons you want to study and review them in your sequence of choice to enhance your knowledge of sets in a manner that works for you. Assess your knowledge of the lessons by taking their multiple-choice quizzes. If you need to clarify details or want additional information about any lesson, feel free to send questions to our experts. Ensure you have a good grasp of all concepts covered in this chapter by taking the comprehensive practice exam.
1. Mathematical Sets: Elements, Intersections & Unions
Today we're going to explore mathematical sets, which are surprisingly simple! Sets are just collections of any objects or concepts, also known as elements, that can be related to each other through union or intersection.
2. Cardinality & Types of Subsets (Infinite, Finite, Equal, Empty)
In this video, we will add to our knowledge of sets. We will talk about cardinality, infinite, finite, equal and the empty set. I think you will find these very straightforward, so let's begin.
3. How to Find the Cartesian Product
The Cartesian product allows us to take two sets of mathematical objects and create one new one. With one simple idea, the Cartesian product becomes quick and easy.
4. Venn Diagrams: Subset, Disjoint, Overlap, Intersection & Union
The Venn diagram was introduced by John Venn. Yes, the Venn diagram is named after a real person! His idea was to show sets in terms of pictures. The Venn diagram is now used in many fields, including mathematics. Let's take a look at John Venn's idea.
5. Categorical Propositions: Subject, Predicate, Equivalent & Infinite Sets
Watch this video lesson to learn how categorical propositions are written. You will also see what the subject and predicate are as well as learn about equivalent and infinite sets.
6. How to Change Categorical Propositions to Standard Form
Watch this video lesson to learn what categorical propositions are and how you can turn your statements into one of the four standard forms. Also, learn the names of these four standard forms and what they look like.
7. What is a Two-Way Table?
Do you believe in Martians? Do you watch football on television? A Two-Way Table or Contingency Table is a great way to show the results of all kinds of survey questions. In this video we will learn how to read a two-way table.
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Other chapters within the NY Regents Exam - Integrated Algebra: Test Prep & Practice course
- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Exponents
- Problems with Exponential Expressions
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Distributing Terms in Algebra
- Algebraic Linear Equations & Inequalities
- Understanding Matrices & Absolute Value
- Overview of Functions
- Factoring with Variables
- Quadratics & Polynomials
- Rational Expressions & Practice
- Graphing Functions
- Calculations with Ratios, Percent & Proportions
- Understanding Probability & Statistics
- Factorials & the Binomial Theorem
- Working with Data
- Well-Known Equations
- Intro to Trigonometry
- Measurement for Algebra Students
- Geometry for Algebra Students
- About the NY Regents Examinations
- NY Regents Exam - Integrated Algebra Flashcards