# Ch 54: AEPA Middle Grades Math: Sets

### About This Chapter

## AEPA Middle Grades Math: Sets - Chapter Summary

The lessons in this chapter can show you about mathematical sets, subsets, Venn diagrams and categorical propositions as you prepare for the NES Middle Grades Math exam. You'll get information that will help you tackle these topics when you take the exam:

- Working with elements, intersections and unions
- Understanding cardinality and infinite, finite, equal and empty subsets
- Finding the Cartesian product
- Creating Venn diagrams
- Using categorical propositions
- Changing categorical propositions to standard form

You'll gain a mastery of the concept of sets and subsets, guided by our expert instructors. These brief lessons make learning fun as you prepare for the test.

### AEPA Middle Grades Math: Sets - Chapter Objectives

The AEPA Middle Grades Math test is required to obtain an Arizona license to teach middle school math. The test covers concepts including principles of discrete mathematics and techniques for determining probability. Questions on sets are found in the test's section on Statistics, Probability, and Discrete Mathematics, which takes up 25% of the 150-question test.

The AEPA Middle Grades Math test contains multiple-choice questions, offering a problem or query with four possible answers. You can practice taking this type of test with the self-assessment exam found at the end of each of our lessons.

### 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 AEPA Middle Grades Mathematics (NT203): Practice & Study Guide course

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