Name
3-5
Class
Date
Working with Sets
Working With Sets
There are two ways to write a set.
• Roster form lists the elements of a set within braces, {}.
• Set-builder notation describes the properties an element must have to be
included in a set.
Problem
How do you write “R is the set of even whole numbers less than 10” in roster form and in
set-builder notation?
Roster Form
List the numbers 0, 2, 4, 6, and 8 in braces.
R = {0, 2, 4, 6, 8}
Set-Builder Notation
Describe the properties.
R = {x | x is an even whole number, x < 10}
This is read as “R is the set of all numbers x such that x is an even whole number less than 10.”
Exercises
Write each set in roster form and in set-builder notation.
1. D is the set of integers greater than –5 and less than 5.
2. N is the set of odd natural numbers less than 14.
3. P is the set of natural numbers less than or equal to 7.
4. T is the set of real numbers that are factors of 18.
5. A is the set of integers between –3 and 5.
Write the solutions of each inequality in set-builder notation.
6. 4b + 8 > –12
7. 7n – 14 ≥ 28
8. 5s – 15 ≤ 18 – 2s
9. 2(3p – 5) – 7p < –2
Page 1
Name
3-5
Class
Date
Working with Sets (continued)
Working With Sets
Set A is a subset of set B if each element of A is also an element of B.
Problem
What are all the subsets of the set {r, s, t}?
0
Start with the empty set because it is a subset of every set.
{r}, {s}, {t}
Each element of the given set is a subset of the given set, so list the
subsets with one element.
{r, s}, {r, t}, {s, t}
List the subsets with two elements from the given set.
{r, s, t}
List the original set. It is always a subset of itself.
The subsets of {r, s, t} are 0 , {r}, {s}, {t}, {r, s}, {r, t}, {s, t} and {r, s, t}.
Exercises
List all the subsets of each set.
10. {5, 10}
11. {mom, dad, child}
12. {–2, –1, 0}
13. {a, b, c, d}
The universal set U is the set containing all of the elements in a problem. The
complement of a set S is the set of all the elements in the universal set but not in the
set S. The complement of S is written S'.
Problem
If U = {days of the week} and D = {Sunday, Friday}, what is D'?
The days of the week that are not in D are Monday, Tuesday, Wednesday,
Thursday, and Saturday.
D' = {Monday, Tuesday, Wednesday, Thursday, Saturday}
Exercises
14. If U = {natural numbers less than 20} and N = {factors of 18}, what is N'?
15. If U = {months of the year} and M = {months starting with J}, what is M'?
Page 2