unit 1 mathematical terminology & notation. work with sets standard 25.0

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