Sets and Set Notation

What are sets?

A set is a collection of things. The "things" in the set are called the "elements”.

A set is represented by listing all the elements of the set.

EX: Set of colors in the rainbow

The elements of this set are red, orange, yellow ,green, blue, indigo, & violet.

{red, orange, yellow, green, blue, indigo, violet}

Sets are written using the roster method.

Now the elements of our set are written:

There has to be more to it than that!Universal set: Set of all elements under consideration.

Denoted by capital U

U = {red, orange, blue, green, indigo, yellow}

A = {red, green, blue}

Subsetsare parts of the universal set. They are labeled by capital letters

UA Subset symbol

A picture representation looks like this

AU

red A : means red is an element of set A

Symbol for element

U = set of all real numbers

B

UA UB

natural #’sA

The Symbols for numbers include:

These can be used to write our solutions to equations in a funky way!

10 xZxx ,

I digress….more on that later in the year. Two other important aspects of sets:

1. Union of sets:

A B

BA

Symbol for Union or joining of sets is skatingpilatesyogafootballgolfracingBA ,,,,,

2. Intersection of sets DC C = {1, 3, 5, 7, 9, 11}D = {3, 6, 9, 12, 15}

3 6 9 12 15

18

1 3 5 7 9 11

1 5 3 7 9 11

6 12 15

18

C

D

93, DC

Definitions: Sets: are collections of clearly identified objects.

Universal set is the collection of all objects under discussion.

Subsets: part of the original set

Complements of sets are elements of one set or the universal set

but not included in the subset. Ac or  A' or ~A or means the complement of set A

A

Union of sets is the combining of sets to form a new set. means union of sets A and BBA

Intersection of sets is a set of all elements common to both sets.

means intersection of sets A and B BA

The roster method has sets identified by capital letters. Each element of the set is listed between braces and separated by commas only. A set which has three ellipses on either end indicates the set continues in that direction.

.

Elements of sets are the individual things within a set.

means 5 is an element of set A

A5

Examples. Use the set of natural numbers for the following.The universal set: U is ______________________________________

1. Write the set of numbers between 6 and 20 A: ________________________________________

2. Write the set of natural numbers which are multiples of 5 Label it B.

B:__________________________________________

3. Write a set which is a complement of set B. Label it C.

C: _________________________________________