Week 3

1. Take out your name tag2. Take out the writing utensils3. Put your backpack away4. Work on the warm up5. Check the agenda on the board6. Put your homework on the desk

Unit 1 Mathematical Terminology

& Notation

Work with Sets

Standard 25.0

Standard 25.0Students use properties from number systems to justify steps in combining and simplifying functions.Objectives:• I can use different set notations to represent

the number system.• I can find the union and intersection of two

sets and justify the solution.

Definition

• Set– A well-defined collection of distinct objects

• Element– An object in a set– Example:

• Empty set or null set– A set has no elements ()

VocabularySet Elements Empty set Null set

Subset Intersection Union Universal set

Complement Rational number Irrational number

Examples

• Set of digits– Collection of 0 – 9Roster Method

Set-builder Notation

Read: D is the set of all x such that x is a digit

element

Practice 1

• E is a set of even digitRoster Method

Set-builder Notation

Read: E is the set of all x such that x is an even digit

Practice 2

• O is a set of odd numberRoster Method

Set-builder Notation

Read: O is the set of all x such that x is an odd digit

Subset

• Subset C– If every element of a set A is also an element of a

set B, then we say that A is a subset of B.

Example: C

AB

14 2

3

5

Write a daily life example involving subset.

Equals

– If two sets A and B have the same elements, we say that A equals B, A = B.

Example: =

Intersection & Union

• If A and B are sets, the intersection of A with B, denoted .– The set consisting of elements that belong to both

A and B• Union– The set consisting of elements that belong to

either A or B, or both.

A B

A B

Write a daily life example involving intersection and one example for union.

Example

Let , , and . Find:(a) (b) (c)

¿ {4,6 }¿ {2,4 ,5,6,7 }¿∅

Example

Let , , and . Find.(a) (b) (c)

Solution

Let , , and . Find.(a) = = (b) = = (c) = = =

Universal Set & Complement

• Universal Set U• The set of all the elements that we wish to

consider• Complement or A’– The set consisting of all the elements of the

universal set not found in a given set.

Example

If the universal set is and if , then .

Definition of complement and

Example

If the universal set is and if , then .

If the universal set is and if , then .

Venn Diagrams

• Subset ACB

B

A

Universal set

Venn Diagrams

• Disjoint sets

BA

Universal set

Venn Diagrams

• Intersection

BA

Universal set

Venn Diagrams

• Union

BA

Universal set

Venn Diagrams

• Complement

𝐴A

Universal set

Practice

, ,

Homework (due Friday)

, ,

Foldables (due on 8/22 Wed)Set Subset

Union Intersection

Complement Empty Set /Null Set

Cover: 6 vocabularyLevel 1: Definition + DrawingLevel 2: 1 real-life example + 1 math example

Set Up Binder

Label the 6 dividers as below:1. Warm Up2. Tests3. Unit 14. Unit 25. Unit 36. Unit 4

Homework Policy

1. Homework will be due according to the deadline stated, at the beginning of class

2. If you did not do the homework before class starts, I will keep you after class to finish your work

3. By Thursday nutrition, if you have any missing homework for the week, you will be given mandatory tutoring notice during 4th period, and you will need to stay for office hours after school on Thursday

4. If you do not show up at the office hour after receiving the notice, you will receive two detention hours