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Math 102: College Mathematics14 chapters | 108 lessons

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Lesson Transcript

Instructor:
*Kathryn Maloney*

Kathryn teaches college math. She holds a master's degree in Learning and Technology.

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.

A **set** is a collection of objects, and it doesn't need to be a number!

This is the set of the clothes in my closet: *C* = {pants, t-shirt, skirt, and dress}. The capital *C* represents the set. So, if I said set *C*, we know I'm talking about clothes in my closet. The braces, { }, denote the elements, or members of the set. The elements of set *C* are pants, t-shirt, skirt, and dress.

You're probably familiar with a set of real numbers: *R* = {â€¦-3, -2, -1, 0, 1, 2, 3...}. The three dots indicate that the pattern continues. The elements of this group are all real numbers. So, *R* equals the set of real numbers.

To collect sets together, we use the term **union**. We *unite* the sets into one.

Let's say I have two sets. Set *A* is green, blue, and pink. Set *B* is orange, yellow, and black. *A u B* represents the union of sets *A* and *B*. Yes, that *u* symbol represents union! It's kind of handy! *A u B* represents all the elements that are listed in set *A*, or in set *B*, or in both. How would that look in using mathematical symbols? *A u B* = {green, blue, pink, orange, yellow, black}.

To find elements in common with sets, we use the term **intersection**. Think of the sets as two roads that meet at an intersection. What do the two roads, or sets, have in common?

Let's say I have two sets. Set *A* is 4, 6, and 9. Set *B* is 7, 8, and 9. *A* intersect *B* represents the intersection of sets *A* and *B*. Yes, that upside down *u* represents intersection! This represents all the elements that are the same in *A* and *B*. How would that look in using mathematical symbols? *A* intersect *B* = {9}.

Let's review what we just talked about. A **set** is a bunch of objects. It could be numbers, letters, anything. To show a set, we always use a capital letter. To show the members, or the elements, of a set, they always go between braces, { }, or these curlicue parentheses. **Union** is when we unite things - when we're going to put things together. So, *A u B* means that we're going to put everything in *A* together with everything in *B*. Remember, **intersection** is where things are the same - where they intersect at. So, if I say *A* intersect *B*, what I'm looking for is any elements, or members, that are common in *A* and *B*.

After watching this lesson, you should be able to identify concepts of sets, such as elements, and how they're related through union and intersection.

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Math 102: College Mathematics14 chapters | 108 lessons

- Go to Logic

- Mathematical Sets: Elements, Intersections & Unions 3:02
- How to Find the Cartesian Product 3:57
- Venn Diagrams: Subset, Disjoint, Overlap, Intersection & Union 6:01
- Categorical Propositions: Subject, Predicate, Equivalent & Infinite Sets 4:24
- How to Change Categorical Propositions to Standard Form 3:28
- What is a Two-Way Table? 3:40
- Go to Sets

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