# 1.2 Sets and set notation pt.2

Good morning!
Schedule:
• Learning goals
• Homework
• Problem solving question
• Revision: Sets and Set notation
• Properties of real numbers + homework
1 / 23
Slide 1: Slide
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This lesson contains 23 slides, with interactive quizzes and text slides.

## Items in this lesson

Good morning!
Schedule:
• Learning goals
• Homework
• Problem solving question
• Revision: Sets and Set notation
• Properties of real numbers + homework

#### Slide 1 -Slide

Learning goals
At the end of this lessons I can:
• Name the properties of number sets
• round to different degrees of accuracy

#### Slide 2 -Slide

Any homework questions?

#### Slide 3 -Mind map

Problem solving strategies

#### Slide 4 -Slide

Problem solving strategies
- Take 1
- Easy numbers
- Draw it!
- Working backwards

#### Slide 5 -Slide

Problem solving question

#### Slide 6 -Slide

Which strategy did you use?

#### Slide 7 -Mind map

Set Theory symbols

#### Slide 8 -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 9 -Slide

Sets and set notation
A = { all positive even numbers } , B =  {x : x ∈ N, x < 5}, C = {10, 20, 30, 40}
The universal set U = {all Natural numbers} or ℕ
True or false?
1. C ⊂ A
2. Ø ⊆ B
3. 0 ∈ A
4. A' = {all positive odd numbers}
5. B ⊆ A

#### Slide 10 -Slide

A = { all positive even numbers } , B = {x : x ∈ N, x < 5}, C = {10, 20, 30, 40}
The universal set U = {all Natural numbers} or ℕ
True or false?
1. C ⊂ A
A
True
B
False

#### Slide 11 -Quiz

A = { all positive even numbers } , B = {x : x ∈ N, x < 5}, C = {10, 20, 30, 40}
The universal set U = {all Natural numbers} or ℕ
True or false?
2. Ø ⊆ B
A
True
B
False

#### Slide 12 -Quiz

A = { all positive even numbers } , B = {x : x ∈ N, x < 5}, C = {10, 20, 30, 40}
The universal set U = {all Natural numbers} or ℕ
True or false?
3. 0 ∈ A
A
True
B
False

#### Slide 13 -Quiz

A = { all positive even numbers } , B = {x : x ∈ N, x < 5}, C = {10, 20, 30, 40}
The universal set U = {all Natural numbers} or ℕ
True or false?
4.A' = {all positive odd numbers}
A
True
B
False

#### Slide 14 -Quiz

A = { all positive even numbers } , B = {x : x ∈ N, x < 5}, C = {10, 20, 30, 40}
The universal set U = {all Natural numbers} or ℕ
True or false?
5.B ⊆ A
A
True
B
False

#### Slide 15 -Quiz

Sets and set notation
A = { all positive even numbers } , B =  {x : x ∈ N, x < 5}, C = {10, 20, 30, 40}
The universal set U = {all Natural numbers} or ℕ
True or false?
1. C ⊂ A
2. Ø ⊆ B
3. 0 ∈ A
4. A' = {all positive odd numbers}
5. B ⊆ A

#### Slide 16 -Slide

Homework
P. 26: Practice 3(1, 2, 3, 4

#### Slide 17 -Slide

Properties of real numbers (addition and multiplication)

If you want more explanation, open this Lessonup from Toddle > Class files > Unit 1 number systems and number sense
And go to Slide 19

Done?

Homework:
P. 26: Practice 3(1, 2, 3, 4)
P. 30: Practice 4

#### Slide 18 -Slide

Properties of real numbers: Commutative property

The Property:                       a + b = b + a
a ⋅ b  = b ⋅ a

Example:                                2 + 3 = 3 + 2
2 ⋅ 3 = 3  ⋅ 2
Is there a different operator that does not have this property?

#### Slide 19 -Slide

Properties of real numbers: Associative property

The Property:                       a + (b + c) = (a + b) + c
(a ⋅ b) ⋅ c  = a ⋅ (b ⋅ c)

Example:                                1 + (2 + 3) = (1 + 2) + 3
1 ⋅ (2 ⋅ 3) = (1 ⋅ 2) ⋅ 3
Is there a different operator that does not have this property?

#### Slide 20 -Slide

Properties of real numbers: Identity

The Property:                                  a + i = a
a ⋅ i = a

What is the identity for the set of real numbers under addition ?
What is the identity for the set of real numbers under multiplication?

#### Slide 21 -Slide

Properties of real numbers: Inverse

The Property:                                  a + Inv = i  (i = 0)
a ⋅ Inv = i  (i = 1)

What is the inverse for the set of real numbers under addition ?
What is the inverse for the set of real numbers under multiplication?

#### Slide 22 -Slide

Properties of real numbers: Distributive property

The Property:                       (a + b)c = ac + bc

Example:                                (20 + 7)4 = 80 + 28