# Ch 50: GACE Middle Grades Math: Sets

### About This Chapter

## GACE Middle Grades Math: Sets - Chapter Summary

In this chapter, our instructors introduce types of sets and subsets as well as examine the key concepts of mathematical sets. Lesson topics include the following:

- Defining the elements, intersections and unions of sets
- Identifying types of subsets
- Finding the Cartesian product
- Using Venn diagrams
- Defining categorical propositions
- Changing categorical propositions to standard form

The instructors, experts in the math field, offer content-rich lessons and engaging visuals to make studying mathematical sets fun. Each lesson is less than 10 minutes long and can be watched anytime on your computer, smart phone or tablet. Many videos include links to text lessons providing additional detail about key terms. Be sure to take the multiple choice quizzes to test yourself on how well you grasped lesson materials.

### 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 GACE Middle Grades Mathematics (013): Practice & Study Guide course

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