Introduction to SETS

SETS

Applied Math

Multiple Select

WARM UP Which of the following are sets ?  WHY?

• The collection of good books.

•  The collection of prime numbers less than 30

• The collection of ten most talented mathematics teachers.

• The collection of all students in your school.

• The collection of all even numbers.

​Essential Questions

• ​What is the purpose of sets and why do we use them?h

• ​How do define the three types of sets?

• ​How can we read given a set of data what type of set we should use?​

Poll

When you go to the Grocery Store DO YOU??

• Make a list

• Just buy whatever?

​The purpose of Sets

• ​To help us keep things in order.

• ​The basis of all mathematics

• ​Provide us with a visual.

• ​Help organize data​

Multiple Choice

Which of the following is a well-defined set?

• honest students

• popular actors

• rainbow colors

• favorite subjects

​Roster Set

Roster Notation

​The elements of a set are represented in a row surrounded by curly brackets and if the set contains more than one element then every two elements are separated by commas.

EXAMPLE: if A is the set of first 10 natural numbers so it can be represented by:

Multiple Choice

Which one of these represents a roster set

• A = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100}

• {y : y > 0}

• Set B is the set of all natural numbers less than 15.

• A = {a, b, c} and B = {b, c, d}

​Why Do We Use Roster Notation?

• ​Roster notation is one of the most simple techniques to represent the elements of a set.

• ​The elements can be represented in a row and are easy to read and understand.

Verbal Description

Uses an English sentence to state a rule that allows us to determine the class of objects being discussed and to determine for any particular object whether or not it is in the set.

​EXAMPLE:

​

​The Set of all Vowels in the Alphabet

​

​The Set of all counting numbers less than 5.

​Why Do We Use Verbal descriptions

• ​Allows us to determine the class of objects being discussed

• ​Determines for any particular object whether or not it is in the set.

Set Builder Notation

Set Builder Notation Example 2

​Set Membership

• ​We use the symbol ∈ to show that an object is a member of a set. The symbol is read as ‘is an element of’ or ‘is a member of.’​

• B = { 1, 2, 3, ​4 } 1 is an element of B so we write it 1 ∈ B

• We use the symbol ∉ to show that an object is not a member of a set. The symbol is read as ‘is not an element of’ or ‘is not a member of.’​

​Classification of SETS

• Empty set​ ∅ Contains no elements ∅ = { }

• ​Finite set - a set that has a finite number of elements P = { 0, 3, 6, 9, …, 99}

• ​Infinite set - has no finite number of elements A set of all whole numbers, W= {0, 1, 2, 3, 4,…}

• ​Subset - a set A is a subset of a set B if all elements of A are also elements of B

Multiple Choice

The elements of a set are separated by a

• Equal to

• Comma

• Semi colon

• Full stop

Multiple Select

If A is the set of even numbers less than 10, which elements belong to this set?

• 3

• 6

• 0

• 8

Multiple Choice

If A = {even numbers less than 13}, then

• A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

• A = {1,3, 5, 7, 9, 11}

• A = {2, 4, 6, 8, 10, 12}

• A = {2, 4, 6, 8, 11,}

Multiple Select

∈ = Integers between 1 and 20 inclusive.

Describe the following set...

{2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

Select all that apply...

• multiples of 2

• multiples of 3

• even numbers

• odd numbers

Multiple Choice

∈= Integers between 1 and 20 inclusive.

Describe the following set...

{1, 2, 5, 10}

• multiples of 2

• factors of 5

• factors of 10

• multiples of 10