# Ch 55: ORELA Middle Grades Math: Sets

### About This Chapter

## ORELA Middle Grades Math: Sets - Chapter Summary

These videos are taught by experienced instructors who present the properties and steps for solving problems with sets such as elements, intersections and unions. Watch the video lessons to prepare for ORELA Middle Grades Math exam questions on:

- Types of mathematical sets and subsets
- Cardinality
- Cartesian product
- Venn diagrams
- Categorical propositions

These video lessons are designed to help you brush up on the topics covered on this teacher licensing exam. The videos present key math topics in an entertaining way with graphics and real-life examples, and supplementary transcripts and multiple-choice quizzes are available to help reinforce the concepts and help familiarize you with the test format.

### ORELA Middle Grades Math: Sets Objectives

The ORELA Middle Grades Math exam is a four hour and 15 minute test that includes 150 multiple-choice questions. The test includes questions from multiple domain areas within math, and the topics covered in this chapter are covered within the statistics, probability and discrete mathematics domain. This domain area makes up about 25% of the test questions and may ask you apply set theories to solve problems. You can use the lessons in this chapter to prepare for questions on sets, subsets and more, as well as use the short quizzes to practice for test day.

### 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.

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### Other Chapters

Other chapters within the ORELA Middle Grades Mathematics: Practice & Study Guide course

- ORELA Middle Grades Math: Basic Arithmetic Operations
- ORELA Middle Grades Math: Solving Math Word Problems
- ORELA Middle Grades Math: Properties of Numbers
- ORELA Middle Grades Math: Estimating & Rounding
- ORELA Middle Grades Math: Number Theory
- ORELA Middle Grades Math: Roots & Radical Expressions
- ORELA Middle Grades Math: Exponents & Exponential Expressions
- ORELA Middle Grades Math: Scientific Notation
- ORELA Middle Grades Math: Simplifying Whole Number Expressions
- ORELA Middle Grades Math: Integers
- ORELA Middle Grades Math: Rational Numbers
- ORELA Middle Grades Math: Introduction to Fractions
- ORELA Middle Grades Math: Operations with Fractions
- ORELA Middle Grades Math: Introduction to Decimals
- ORELA Middle Grades Math: Operations with Decimals
- ORELA Middle Grades Math: Percents
- ORELA Middle Grades Math: Money & Consumer Math
- ORELA Middle Grades Math: Number Patterns & Sequences
- ORELA Middle Grades Math: Properties of Functions
- ORELA Middle Grades Math: Graphing Functions
- ORELA Middle Grades Math: Negative Numbers
- ORELA Middle Grades Math: Absolute Value
- ORELA Middle Grades Math: Inequalities
- ORELA Middle Grades Math: Factoring
- ORELA Middle Grades Math: Monomials & Polynomials
- ORELA Middle Grades Math: Writing Algebraic Expressions
- ORELA Middle Grades Math: Basic Algebraic Expressions
- ORELA Middle Grades Math: Algebraic Distribution
- ORELA Middle Grades Math: Writing & Solving One-Step Equations
- ORELA Middle Grades Math: Writing & Solving Two-Step Equations
- ORELA Middle Grades Math: Simplifying & Solving Rational Expressions
- ORELA Middle Grades Math: The Coordinate Graph
- ORELA Middle Grades Math: Linear Equations
- ORELA Middle Grades Math: Systems of Linear Equations
- ORELA Middle Grades Math: Rates, Ratios & Proportions
- ORELA Middle Grades Math: Measurements
- ORELA Middle Grades Math: Perimeter & Area
- ORELA Middle Grades Math: Polyhedrons & Geometric Solids
- ORELA Middle Grades Math: Symmetry, Similarity & Congruence
- ORELA Middle Grades Math: Properties of Lines
- ORELA Middle Grades Math: Angles
- ORELA Middle Grades Math: Triangles
- ORELA Middle Grades Math: Triangle Theorems & Proofs
- ORELA Middle Grades Math: Similar Polygons
- ORELA Middle Grades Math: The Pythagorean Theorem
- ORELA Middle Grades Math: Quadrilaterals
- ORELA Middle Grades Math: Circles
- ORELA Middle Grades Math: Circular Arcs & Measurement
- ORELA Middle Grades Math: Transformations
- ORELA Middle Grades Math: Data & Graphs
- ORELA Middle Grades Math: Statistics
- ORELA Middle Grades Math: Data Collection
- ORELA Middle Grades Math: Samples & Populations
- ORELA Middle Grades Math: Probability
- ORELA Middle Grades Mathematics Flashcards