Name: ______________________________ Date: ___________
Period: ______ Algebra I.
TOPIC I: Set Theory
What you’ll learn: Perform set operation: union, intersection, complement, and cross product.
Use Venn diagram, union and intersection.
Did you remember?
Natural Numbers:
Whole Numbers:
Integers:
Rational Numbers:
Irrational Numbers:
Real Numbers:
A set is_______________________________________________________________________
________________________________________________________________________.
C= {a, e, i, o, u}
Braces
Capital Letters such as A, B, C...
Note: There is two ways to write a set:
Set-Builder notation:
Roster Form:
1
Example: 1: The set of all numbers x such that x is a natural number.
Roster form N= {1, 2, 3, 4, 5,…}
Set-builder notation N= {x|x is a natural number} and it reads the set of all numbers x such
that x is a natural number.
Your turn: Write the set in roster form and in set-builder notation:
M is the set of integers that are greater than  4
Answer: Roster form:
Set-builder notation:
Note:
A subset is a set whose elements are also contained in another set. The symbol  means “is a subset of”
“.
B
A
A  B and the empty set is a subset of any set. Ø  A
Empty Set: There are no elements in the set. The empty set is a subset of any set.
Example 1: Given the sets Let A={1,2,3,4,5….} and B={1,3,5,7…}.Is B a subset of A?
Answer: _____________________________
3.8 Intersection:
Intersection:
Example: Given the sets A= {1, 2, 3, 4, 5} and B= {2, 4, 6, 8}.Find A  B. Draw a Venn Diagram.
Answer:
A B  
Your turn: Given the sets.

M  17,27,37,47,57and N  7,14,27,34,37 . Find M  N .Draw a Venn
Diagram.
2
Union:
Example: Given the sets.
A  1,2,3,4,5and B  2,4,6,8 Find A  B .Draw a Venn Diagram.
Answer: AUB
Your Turn: Given the sets
T  7,8,9,10and S  2,4,6,7,8,10,12,14 Find T  S. Draw Venn Diagram.
Universal Set: It is a set which contains all elements being considered in the given problem. Notation U.
Example: U= {a, b, c, d, e, f} A= {a, c, b} B= {e, b, a}. Complete the Venn Diagram
A  B=
U
A
B
A  B=
Note:
Complement of a set A is the set of all elements in the given universal set U that are not in set A.
Notation A’
Example: Given the set U= {a, b, c, d, e, f} , A= {a, c, b} and B= {e, b, a}Find A’
A’=
Your turn
B’=
3
Now is your turn
Problem 1: At Vanessa’s high school, 32 girls play volleyball and 35 girls play basketball. Of these, 11 play
both volleyball and basketball.Which of these diagrams best represents these numbers?
A
C
Volleyball
Basketball
3
24
Volleyball
13
11
10
21
B
Basketball
Volleyball
11
D
Basketball
32
Basketball
11
Volleyball
Basketball
21
35
11
24
11
Problem 2: The Venn diagram below shows the number of students, out of a class of 30, who earned an A
in mathematics (M) and an A in English (E). How many students:
13
1. Earned an A in mathematics?
M
2. Earned an A in English?
E
7
3. Earned an A in both mathematics and English?
4
6
4. Did NOT earn an A in math and did NOT earn an A in English?
5. Earned an A in math but NOT English?
6. Earned an A in English but NOT in math?
Problem 3: This Venn Diagram shows salad topping used for 100 salads in a cafeteria. B=bacon,
CH=cheese, CR=croutons
How many salads had:
Bacon
11
9
7
10
Cheese
12
1. Just bacon as a topping?
2. Just bacon and cheese?
25
3. Just croutons and bacon?
4. All three topping?
5. No topping?
8
Croutons
CCCroROUTONS
The Cartesian product (Cross Product) AXB (read “A cross B”) of two sets A and B is defined as the
set of all order pairs (a, b) where “a” is a member of A and “b” member of B.
Example If A = {1, 2, 3} and B = {a, b} find AXB
So AXB =
4