The Union and Intersection of Sets

Primary tabs

Lesson Summary: 
In this lesson we define the union and intersection of two sets. A union of two sets is another set whose elements are in either of the original two sets. An intersection of two sets is another set whose elements have to be in both of the original two sets.
Lesson Inputs: 
Sets and Set Notation
Lesson Outputs: 
Open and Closed Intervals

SAMPLE LESSON

Sign in for easy to read lessons narrowly focused on a specific subject. All lessons are linked to each other allowing you to easily see the connections between different Calculus concepts. Our unique Calcmap will give you a bird's-eye view of all our lessons and help you see how important concepts are related to each other. All of the formulas are available to our subscribers, but here is a sample of the lesson you will see when you log in:



Lesson: 

There are many different ways to combine two sets together. Union and Intersection are two methods for combining two sets together that everyone must know. In fact, there is a good chance that you have already learned this from a high school math course.

First, let's define the union of two sets. Let's say we have the sets $A$ and $B$. The union of $A$ and $B$ is a new set we will call $U$ (for union). Here is the definition:

Union of Two Sets $A$ and $B$
The union of two sets $A$ and $B$ is another set whose elements can be in either $A$ or $B$. In other words, if <Sign in to see all the formulas>, then <Sign in to see all the formulas> or <Sign in to see all the formulas>. In set notation we would say that

<Sign in to see all the formulas>


We denote union by the symbol $\cup$ so that <Sign in to see all the formulas>.

Next, let's define intersection. The intersection of $A$ and $B$ is a new set we will call $I$ (for intersection). Here is the definition:

Intersection of Two Sets $A$ and $B$
The intersection of two sets $A$ and $B$ is another set whose elements are in both $A$ and $B$. In other words, if <Sign in to see all the formulas>, then <Sign in to see all the formulas> and <Sign in to see all the formulas>. In set notation we would say that

<Sign in to see all the formulas>


We denote intersection by the symbol $\cap$ so that <Sign in to see all the formulas>.