Set Difference

My report in Math Major 10

1. SET DIFFERENCE

2. Set:
A = {1, 3, 2, 5}
n(A) = | A | = 4

Sets use “curly” brackets
The number of elements
in Set A is 4
Sets are denoted by
Capital letters
A3Î
A7Ï
3 is an element of A
7 is not an element of A

3. A set is a distinct collection of objects. The objects are
called elements.
{1, 2, 3, 4} = {2, 3, 1, 4}
Order does not matter. If a set
contains the same elements as
another set, the sets are equal.
{1, 3, 2, 3, 5, 2}We never repeat elements in a set.{1, 3, 2, 5}

This symbol means "is a subset of"
This is read "A is a subset of B". A Ì B
A = {1, 2, 3} B = {1, 2, 3, 4, 5}
{1, 2, 3, 5}

In ascending order

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

5. ?

Number of
Elements in Set
Possible Subsets Total Number of
Possible Subsets
1. {A} {A} Æ 2

2. {A , B} {A , B} {A} {B} Æ 4

3. {A , B , C}
{A , B , C} {A , B} {A , C}
{B , C} {A} {B} {C}
Æ
8

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} Æ
16
The number of possible subsets of a set of size n is ?2
n

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

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.
Universal Set
A B
A Ç B = Æ
There are no
elements in
both A and B.
When this is
the case they
are called
disjoint sets.
A
This means the complement of A, and
means the set of all elements in the
universal set that are not in A.
A A