# Ch 12: Sets

### About This Chapter

Watch online video lessons on mathematical sets to learn about set notation, cardinality, Venn diagrams, two-way tables and more. Each lesson is accompanied by a short multiple-choice quiz you can use to check your understanding of these math topics.

## Sets

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!

Final Exam
Chapter Exam

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### Other Chapters

Other chapters within the Math 102: College Mathematics course

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