1. SETS Sets are denoted by Capital letters Sets use “curly” brackets
n(A) = | A | = 4
The number of elements in Set A is 4
7 is not an element of A
3 is an element of A

2. A set is a distinct collection of objects
A set is a distinct collection of objects. The objects are called elements.
Order does not matter. If a set contains the same elements as another set, the sets are equal.
{1, 2, 3, 4} = {2, 3, 1, 4}
{1, 3, 2, 5}
{1, 3, 2, 3, 5, 2}
{1, 2, 3, 5}
We never repeat elements in a set.
In ascending order
This symbol means "is a subset of"
A  B
This is read "A is a subset of B".
A = {1, 2, 3} B = {1, 2, 3, 4, 5}

3. It is agreed that the empty set is a subset of all other sets so:
If a set doesn't contain any elements it is called the empty set or the null set. It is denoted by  or { } NOT {} 
It is agreed that the empty set is a subset of all other sets so:
List all of the subsets of {1, 2, 3}. 
{1}
{2}
{3}
{1, 2}
{1, 3}
{2, 3}
{1, 2, 3}
Notice the empty set is NOT in set brackets.

4. 2n Number of Elements in Set Possible Subsets
Total Number of Possible Subsets
1. {A}
{A}  
2 
2. {A , B}
{A , B} {A} {B}  
4 
{A , B , C} {A , B} {A , C} {B , C} {A} {B} {C} 
8 
3. {A , B , C}
4. {A , B , C, D}
{A , B , C , D} {A , B , C} {A , B , D} {A , C , D} {B , C , D} {A , B} {A , C} {A , D} {A , B} …… {D} 
?  16 2n
The number of possible subsets of a set of size n is ?

5. A = {1, 2, 3, 4, 5} B = {1, 3, 5, 7, 9}
Remember we do not list elements more than once.
A  B
= {1, 2, 3, 4, 5, 7, 9}
This is the union symbol. It means the set that consists of all elements of set A and all elements of set B.
A  B
= {1, 3, 5}
This is the intersect symbol. It means the set containing all elements that are in both A and B.

6. These sets can be visualized with circles in what is called a Venn Diagram.
A  B
A  B
Everything that is in A or B.
Everything that is in A AND B.

7. Often will have a set that contains all elements that we wish to consider. This is called the universal set. All other sets are subsets of this set.
A  B = 
There are no elements in both A and B. When this is the case they are called disjoint sets.
Universal Set A A B A
This means the complement of A, and means the set of all elements in the universal set that are not in A.

8. 100 people were surveyed. 52 people in a survey owned a cat
100 people were surveyed. 52 people in a survey owned a cat. 36 people owned a dog. 24 did not own a dog or cat.
Draw a Venn diagram.
Since 24 did not own a dog or cat, there must be 76 that do.
= 88 so there must be = 12 people that own both a dog and a cat.
universal set is 100 people surveyed 24 C D 12 40 24
n(C  D) = 76
Set C is the cat owners and Set D is the dog owners. The sets are NOT disjoint. Some people could own both a dog and a cat.
This n means the number of elements in the set