Mathematical Sets: Elements, Intersections & Unions

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  • 0:10 Understanding Sets
  • 0:55 Unions
  • 1:37 Intersections
  • 2:18 Lesson Summary
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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.

Understanding Sets

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 = {…-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?

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