Set Builder Notation
In this lesson we will go through a few exercises to help you fully understand and capable of writing set builder notation for different types of sets.
First, consider the following set;
{1,2,3,…,99}
Here are the steps to write this in set builder notation:
- First, think about which set do all these elements belong to. These are all natural numbers since they start from 1.
- Second, identify which condition satisfies all of these, and only these functions. This is simply an understanding that all of these numbers are less than 100.
We can write this set in the set builder form like this.
{x∣x∈N∧x<100} Hover over an element to see its meaning
All set builder components have the following components in order.
- A Starting Bracket {
- Creating a Variable x
- Identify which type of variable ∣x∈N (Could be any other set like real numbers or integers)
- An and symbol or some other symbol such as ∧
- One or more conditions such as x<100
- A Closing Bracket - }
Set Builder Notation with Two Conditions
Now let's look at a set builder notation that requires two conditions.
{2,3,…,99}
Here are the steps to write this in set builder notation:
- First, we identify that these are still natural numbers
- Second, we identify that we need two conditions. First, we know that these numbers are less than hundred, but also greater than one.
{x∣x∈N∧x>1∧x<100} Hover over an element to see its meaning
Usually, we combine a conditional like x>1∧x<100 into one form by identifying that x lies in between the two numbers. We can write it as; 1<x<100
A good way to understand this might be:
x>1∧x<100
1<x∧x<100
1<x<100
Set Builder Notation With Integers
Consider the following set.
{−3,−2,−1,0,1,2,3}
Here are the steps to write this in set builder notation:
- First, we identify that these are integers represented as Z.
- Second, we identify that we need two conditions. First, we know that these numbers are greater than or equal to -3 and they are less than or equal to 3.
{x∣x∈Z∧−3≤x≤3} Hover over an element to see its meaning
With these examples, you are ready to create your own set builder notations using this next drag and drop exercises. Good luck!
Build the Correct Equations Activity
{1,2,3,…,1000}
{0,1,2,…,99}
{0,±1,±2,…,±100}
{0,−1,−2,…,−300}
{100,101,…,200}
{−100,−101,−102,…,−200}
Creating Tabular Description from Set Builder
Now let's do the opposite where we read a given set builder and match it with the correct tabular form.
Activity: Match The Columns!
Reorder the Tabular Notation to match them with the correct Set Builder Notation.
{x∣x∈N∧x<5}
{x∣x∈W∧x≤3}
{x∣x∈Z∧−2≤x≤2}
{x∣x∈N∧x is even∧x≤10}
{x∣x∈N∧x is odd∧x<10}
{x∣x∈N∧x>10}