About This Chapter
What is a set? Well, the world can be divided into sets. Have you ever taken pictures to help chronicle an experience? Those very pictures represent a set of your own choosing. In mathematics, a set is a collection of objects. Each object is called an element of that set - they don't necessarily have to be numbers all the time, but we'll show you how to classify and manipulate those elements. Sets aren't always disjoint, so our introduction will explore the union and intersection of sets to demonstrate how they may combine and interact.
We'll further explain the interaction of sets with cardinality - just how many pictures did you take to record that once-in-a-lifetime experience? Cardinality refers to the number of elements in a given subset. Did you have a friend taking pictures of the same experience? If your friend took identical pictures, then those pictures would be a subset of your photo album. We'll examine subsets and cover the differences between finite and infinite sets. You'll also explore the mysteries of the empty set.
Our lessons will reveal another way to combine sets using the Cartesian product. In this way, we can build a new set out of our preexisting sets - imagine being able to combine every picture from your friend's album with your own; you'd end up with a collection of photos that looked completely different from either album alone. We'll also study Venn diagrams for a greater understanding of subsets, intersections and unions. By this point, you'll be an expert at discerning between overlapping elements and disjoint ones.
This chapter will also look at categorical propositions, or the reasoning that takes place when looking for a relation between sets. While studying subject and predicate sets, we'll see how to translate their interaction into standard form. Along these lines, we'll also get used to reading and interpreting two-way tables. A picture may be worth a thousand words, but our lessons use both to ensure that you have the fullest understanding of mathematical sets and their capabilities. Thanks for watching!
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 Math 102: College Mathematics course
- Math Foundations
- Linear Equations
- Solving and Graphing Inequalities
- Graphing and Factoring Quadratic Equations
- Complex and Imaginary Numbers
- Properties of Exponents
- Properties of Polynomials
- Simplifying and Solving Rational Expressions
- Properties of Functions
- Logarithms and Exponential Equations
- Probability and Statistics
- Studying for Math 102