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
1 / 23
volgende
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

Take out your diaries/notebook


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. 
When you've finished, raise your hand for the answerssheet. 
(15 min) 
timer
10:00

Slide 10 - Tekstslide

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
 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 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 = { 

Slide 23 - Tekstslide