Post on 17-Jan-2016
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
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
Example
Let , , and . Find:(a) (b) (c)
¿ {4,6 }¿ {2,4 ,5,6,7 }¿∅
Solution
Let , , and . Find.(a) = = (b) = = (c) = = =
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