# 4.1 Set operations

Good morning!
Schedule:
• Homework
• Types of numbers (activity)
• Set symbols matching game
• Sets and set notation
• Practice examples
• Start on the homework
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Slide 1: Tekstslide
WiskundeMiddelbare school

In deze les zitten 23 slides, met tekstslides.

## Onderdelen in deze les

Good morning!
Schedule:
• Homework
• Types of numbers (activity)
• Set symbols matching game
• Sets and set notation
• Practice examples
• Start on the homework

#### Slide 1 -Tekstslide

Learning goals
At the end of these two lessons I can:
• Categorize most numbers in a numerical set
• Represent sets and their operations
• Find the intersection and union of sets

#### Slide 2 -Tekstslide

Homework for Thursday 15-10-2021:
p. 223: All three questions of practice 1

#### Slide 3 -Tekstslide

Types of numbers
You have different types of numbers:
Natural numbers (counting numbers): Positive whole numbers
{0, 1, 2, 3, 4, ...}

All natural numbers =

#### Slide 4 -Tekstslide

Types of numbers
You have different types of numbers:
Integers: Positive and negative whole numbers
{..., -2, -1, 0, 1, 2, 3, ...}
,
All integers =

Every natural number is an integer !

#### Slide 5 -Tekstslide

Types of numbers
You have different types of numbers:
Rational numbers: Numbers you can write as a fraction
for example           ,              , 4
,
All ration numbers=

Every integer is a rational number, therefore every natural number is also a rational number !
43
0.2

#### Slide 6 -Tekstslide

Types of numbers
You have different types of numbers:
Real numbers : All rational and irrational numbers
For example          ,           , -2, 0.9999999....

All real numbers =
43
2

#### Slide 7 -Tekstslide

Types of numbers
1. Read through the 1st page of the handout.
2. Each group will receive 2 notes with numbers on them.
3. Discuss in your group to what numeric set(s) your numbers belong to. (some numbers belong to multiple sets, choose 1).
4. Stick the post-it note on the whiteboard in the set where you think it belongs.
5. When you've finished, copy the chart on the whiteboard

#### Slide 8 -Tekstslide

Sets and set notation
A = { all even numbers between 1 and 10}

A = { 2, 4, 6, 8, 10}
Set
Description of the elements of A
Listing of the elements of A

#### Slide 9 -Tekstslide

Matching game
Match the symbol with the correct meaning.
(15 min)
timer
10:00

Review

#### Slide 11 -Tekstslide

Union and intersection
What are we having for dinner tonight?
A is the set of meals that I like, B is the set of meal that my mom likes.
A = {lasagna, burritos, quiche, pasta carbonara}
B = {chili, curry, quiche, lasagna}
A ∩ B = Intersection of A and B = The meals that both me and my mom likes.

A∪B = The union of A and B = The meals that either me or my mom likes.

#### Slide 12 -Tekstslide

Sets and set notation
if A = { -3, -2, 0, 1, 5}
Then
A+ = {.... }
A- = { ....}
A* = { .... }
Find the elements of these 3 sets.

#### Slide 13 -Tekstslide

Sets and set notation
if A = { -3, -2, 0, 1, 5}
Then
A+ = {1, 5}
A- = {-3, -2}
A* = {-3, -2, 1, 5}

#### Slide 14 -Tekstslide

Universal and complementary set
The complementary set (notation: A' or Ac) of a set A contains all elements that DO NOT belong to A.
The universal set (notation: U) is a set which contains ALL ELEMENTS of a problem.
Example:

If U = { 1, 2, 3, 4, 5} and
A = { 2, 4, 5} then
A' = {1, 3}

#### Slide 15 -Tekstslide

Set and set notation

#### Slide 16 -Tekstslide

Set and set notation
a. A∩B = The intersection of A and B
What elements do                    and                    have in common? None!
A∩B = ∅ (or { })

#### Slide 17 -Tekstslide

Set and set notation
b. A∪B' = The Union of A and the complement of B.
B' = all elements in U that are not in B
B' = {1, 4, 6, 8, 9, 10}
All elements of A and B' together:
A∪B' = {1, 2, 4, 6, 8, 9, 10}        No double values in a set!

#### Slide 18 -Tekstslide

Set and set notation
c. (A' ∩ B)' = The complement of the intersection of A' and B.
A' = {1, 3, 5, 7, 9, 10}
A' ∩ B = {3, 5, 7}
(A' ∩ B)'  = {1, 2, 4, 6, 8, 9, 10}

#### Slide 19 -Tekstslide

Set and set notation
d. (A ∪ B ∪ C)' = The complement of the union of A, B and C.
A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9}
(A ∪ B ∪ C)'  = {10}
When looking for the compliment of a set, Compare the set with the Universal set and find the differences

#### Slide 20 -Tekstslide

Sets and set notation
U is the set of all x such that x is an integer larger or equal to 0 and smaller or equal than 20.
Listing of the elements:
U = {0, 1, 2, 3, 4, 5, ... , 19, 20}

#### Slide 21 -Tekstslide

Homework: Practice 1
How would you describe U? List the elements of U.

And how would you describe C? List the elements of C.

#### Slide 22 -Tekstslide

Homework: Practice 1
U = the set of all positive integers between (and including) 1 and 20
U = { 1, 2, 3, ..., 19, 20}

C = the set of all primes between (and including) 1 and 20
C = {