4.1 Set operations
Good afternoon!
Schedule:
- Homework
- Set symbols whiteboard revision
- Sets and set notation
- Practice examples
- Start on the homework
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Slide 1: Slide
WiskundeMiddelbare schoolvwoLeerjaar 4
This lesson contains 34 slides, with text slides.
Lesson duration is: 60 minItems in this lesson
Good afternoon!
Schedule:
- Homework
- Set symbols whiteboard revision
- Sets and set notation
- Practice examples
- Start on the homework
Slide 1 - Slide
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 - Slide
Take out your diaries/notebook
Homework for Tuesday 10-1-2023:
p. 223: All three questions of practice 1
Slide 3 - Slide
Types of numbers
You have different types of numbers:
Natural numbers (counting numbers): Positive whole numbers
{0, 1, 2, 3, 4, ...}
All natural numbers =
ℕ
Slide 4 - Slide
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 !
ℤ
Slide 5 - Slide
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 !
ℚ
43
0.2
Slide 6 - Slide
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
ℝ
Slide 7 - Slide
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 - Slide
Set notation
What is the Mathematical symbol for....
.. is an element of ..
Slide 9 - Slide
Set notation
What is the Mathematical symbol for....
.. is an element of ..
∈
Slide 10 - Slide
Set notation
What is the Mathematical symbol for....
.. is a subset of ..
Slide 11 - Slide
Set notation
What is the Mathematical symbol for....
.. is a subset of ..
⊆
Slide 12 - Slide
Set notation
What is the Mathematical notation/symbol for....
Listing a set
Slide 13 - Slide
Set notation
What is the Mathematical notation/symbol for....
Listing a set
{ ..., ..., ... }
Slide 14 - Slide
Set notation
What is the Mathematical notation/symbol for....
The empty set
Slide 15 - Slide
Set notation
What is the Mathematical notation/symbol for....
The empty set
{ } or ∅
Slide 16 - Slide
Review
Slide 17 - Slide
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 18 - Slide
Sets and set notation
if A = { -3, -2, 0, 1, 5}
Then
A+ = {.... }
A- = { ....}
A* = { .... }
Find the elements of these 3 sets.
Slide 19 - Slide
Sets and set notation
if A = { -3, -2, 0, 1, 5}
Then
A+ = {1, 5}
A- = {-3, -2}
A* = {-3, -2, 1, 5}
Slide 20 - Slide
Union and intersection
What are we having for dinner tonight?
A is the set of meals that I like, B is the set of meals that my mom likes.
A = {lasagna, burritos, quiche, pasta carbonara}
B = {chili, curry, quiche, lasagna}
Slide 21 - Slide
Union and intersection
What are we having for dinner tonight?
A is the set of meals that I like, B is the set of meals 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.
Slide 22 - Slide
Union and intersection
What are we having for dinner tonight?
A is the set of meals that I like, B is the set of meals 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 23 - Slide
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 24 - Slide
Set and set notation
Slide 25 - Slide
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 26 - Slide
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 27 - Slide
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 28 - Slide
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 29 - Slide
Sets and set notation
Read this as:
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 30 - Slide
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 31 - Slide
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 = { 2, 3, 5, 7, 11, 13, 17, 19}
Slide 32 - Slide
Take out your diaries/notebook
Homework for Tuesday 10-1-2023:
p. 223: All three questions of practice 1
