Set Notation Examples, Practice Questions

January 23, 2025

1

Set notation is a way to express sets (collections of objects, called elements) in mathematics. Below are the common ways to represent sets:

This method lists all the elements of the set.

Example:

$A={1,2,3,4}A = \{1, 2, 3, 4\}$ represents a set containing the numbers 1, 2, 3, and 4.
$B={a,b,c}B = \{a, b, c\}$ represents a set containing the elements “a”, “b”, and “c”.

This method defines a set by a property or rule that its elements must satisfy.

3. Interval Notation:

This method is used to represent a set of real numbers that lies between two endpoints.

Example:

$[1,5][1, 5]$ represents the set of real numbers between 1 and 5, including both 1 and 5.
$(2,6)(2, 6)$ represents the set of real numbers between 2 and 6, excluding both 2 and 6.

Roster Notation: Write the set of all prime numbers less than 10 in roster notation.
Set-builder Notation: Write the set of all even numbers between 1 and 10 (inclusive) using set-builder notation.
Interval Notation: Express the set of all real numbers greater than 3 but less than or equal to 7 in interval notation.
Set Operations: Let A={2,4,6} and B={1,2,3,4}
- Find $A∪BA \cup B$ (the union of A and B).
- Find $A∩BA \cap B$ (the intersection of A and B).
- Find $A-BA - B$ (the difference of A and B).