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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