1. 2.1 – Symbols and Terminology
Definitions:
Set: A collection of objects.
Elements: The objects that belong to the set.
Set Designations (3 types):
Word Descriptions:
The set of even counting numbers less than ten.
Listing method:
{2, 4, 6, 8}
Set Builder Notation:
{x | x is an even counting number less than 10}

2. 2.1 – Symbols and Terminology
Definitions:
Empty Set: A set that contains no elements. It is also known as the Null Set. The symbol is 
List all the elements of the following sets.
The set of counting numbers between six and thirteen.
{7, 8, 9, 10, 11, 12}
{5, 6, 7,…., 13}
{5, 6, 7, 8, 9, 10, 11, 12, 13}
{x | x is a counting number between 6 and 7} 
Empty set
Null set
{ }

3. 2.1 – Symbols and Terminology
∈: Used to replace the words “is an element of.”
∉: Used to replace the words “is not an element of.”
True or False:
3 ∈ {1, 2, 5, 9, 13}
False
0 ∈ {0, 1, 2, 3}
True
-5 ∉ {5, 10, 15, , }
True

4. 2.1 – Symbols and Terminology
Finite and Infinite Sets
Finite set: The number of elements in a set are countable.
Infinite set: The number of elements in a set are not countable
{2, 4, 8, 16}
Countable = Finite set
{1, 2, 3, …}
Not countable = Infinite set

5. 2.1 – Symbols and Terminology
Equality of Sets
Set A is equal to set B if the following conditions are met:
1. Every element of A is an element of B.
2. Every element of B is an element of A.
Are the following sets equal?
{–4, 3, 2, 5} and {–4, 0, 3, 2, 5}
Not equal
{3} = {x | x is a counting number between 2 and 5}
Not equal
{11, 12, 13,…} = {x | x is a natural number greater than 10}
Equal

6. 2.2 – Venn Diagrams and Subsets
Definitions:
Universal set: the set that contains every object of interest in the universe.
Complement of a Set: A set of objects of the universal set that are not an element of a set inside the universal set. Notation: A
Venn Diagram: A rectangle represents the universal set and circles represent sets of interest within the universal set A A U

7. 2.2 – Venn Diagrams and Subsets
Definitions:
Subset of a Set: Set A is a Subset of B if every element of A is an element of B. Notation: AB
Subset or not? 
{3, 4, 5, 6} {3, 4, 5, 6, 8} 
{1, 2, 6} {2, 4, 6, 8} 
{5, 6, 7, 8} {5, 6, 7, 8}
Note: Every set is a subset of itself.
BB

8. 2.2 – Venn Diagrams and Subsets
Definitions:
Set Equality: Given A and B are sets, then A = B if AB and BA. =
{1, 2, 6} {1, 2, 6} 
{5, 6, 7, 8} {5, 6, 7, 8, 9}

9. 2.3 – Set Operations and Cartesian Products
Intersection of Sets: The intersection of sets A and B is the set of elements common to both A and B.
A  B = {x | x  A and x  B}
{1, 2, 5, 9, 13}  {2, 4, 6, 9}
{2, 9}
{a, c, d, g}  {l, m, n, o} 
{4, 6, 7, 19, 23}  {7, 8, 19, 20, 23, 24}
{7, 19, 23}

10. 2.3 – Set Operations and Cartesian Products
Union of Sets: The union of sets A and B is the set of all elements belonging to each set.
A  B = {x | x  A or x  B}
{1, 2, 5, 9, 13}  {2, 4, 6, 9}
{1, 2, 4, 5, 6, 9, 13}
{a, c, d, g}  {l, m, n, o}
{a, c, d, g, l, m, n, o}
{4, 6, 7, 19, 23}  {7, 8, 19, 20, 23, 24}
{4, 6, 7, 8, 19, 20, 23, 24}

11. 2.3 – Set Operations and Cartesian Products
Find each set.
U = {1, 2, 3, 4, 5, 6, 9}
A = {1, 2, 3, 4} B = {2, 4, 6} C = {1, 3, 6, 9}
A = {5, 6, 9}
B = {1, 3, 5, 9)}
C = {2, 4, 5}
(A  C)  B
A  C
{2, 4, 5, 6, 9}
{2, 4, 5, 6, 9}  B
{5, 9}

12. 2.3 – Set Operations and Cartesian Products
Ordered Pairs: in the ordered pair (a, b), a is the first component and b is the second component. In general, (a, b)  (b, a)
Determine whether each statement is true or false.
(3, 4) = (5 – 2, 1 + 3)
True
{3, 4}  {4, 3}
False
(4, 7) = (7, 4)
False

13. 2.3 – Venn Diagrams and Subsets
Shading Venn Diagrams:
A  B A B U A B A B U U

14. 2.3 – Venn Diagrams and Subsets
Shading Venn Diagrams:
A  B A B U U A B A B U

15. 2.3 – Venn Diagrams and Subsets
Shading Venn Diagrams:
A  B A B U A A B A B U U
A  B in yellow

16. 2.3 – Venn Diagrams and Subsets
Locating Elements in a Venn Diagram
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {2, 3, 4, 5, 6} B = {4, 6, 8}
Start with A  B 7 1
Fill in each subset of U. A B 4 2
Fill in remaining elements of U. 3 8 6 5 U 9 10