# 1.2 Sets and set notation

Good morning!
Schedule:
• Learning goals
• Sets and set notation
• Worksheet / Homework
1 / 17
Slide 1: Tekstslide
WiskundeMiddelbare schoolvwoLeerjaar 4

In deze les zitten 17 slides, met interactieve quiz en tekstslides.

## Onderdelen in deze les

Good morning!
Schedule:
• Learning goals
• Sets and set notation
• Worksheet / Homework

#### Slide 1 -Tekstslide

Learning goals
At the end of this lessons I can:
• Classify the different kinds of real numbers
• Represt the different kinds of real numbers
• Describe set in list form and with words
• Use set symbols to describe sets

#### Slide 2 -Tekstslide

What is a set? (definition)

#### Slide 3 -Woordweb

Sets
Definition
A set (noun): a number of things of the same kind that belong or are used together.

#### Slide 4 -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 5 -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 6 -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 7 -Tekstslide

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

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

#### Slide 8 -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
Every number we've talked about so far is a real number

Types of numbers

#### Slide 10 -Tekstslide

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

#### Slide 11 -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 12 -Tekstslide

Worksheet
1. Work on the worksheet

2. When you finish, start on the homework:

Homework
Standard:
P. 22: Practice 1 ALL
P. 24: Practice 2 (1, 2)
Extended:
P. 24: Practice 2 (3)

#### Slide 13 -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 14 -Tekstslide

Subsets and proper subsets
B = {1, 2,}

The subsets of B are:
Ø, {1}, {2}, {1, 2}

Proper subsets of B are:
Ø, {1}, {2}

A subset is more general than a proper subset.
Just like 'green' is more general than 'dark green'.

Every proper subset is a subset.
Set A can only be a Proper subset of set B if set B contains elements that set A doesn't
(so when set A is not equal to set B)

#### Slide 15 -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 16 -Tekstslide

Homework
Standard:
P. 22: Practice 1 ALL
P. 24: Practice 2 (1, 2)
(+)
Extended:
P. 24: Practice 2 (3)

Due Tuesday 20-2!