1.2 Sets and set notation pt.2

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 4

Good morning!

Schedule: 

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

Learning goals 

At the end of this lessons I can:

• Name the properties of number sets
• round to different degrees of accuracy

Any homework questions?

Set Theory symbols

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} 

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

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

Homework

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

Properties of real numbers (addition and multiplication)

Please read the information on P. 30 and do Practice 4. 

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

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? 

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? 

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? 

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? 

Properties of real numbers: Distributive property

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

                                                    

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