Venn Diagram
Venn Diagrams are really great tools for visualizing sets, especially when it comes to how sets intersect and come together.
Set
A collection of "things" (objects or numbers, etc).
Each member is called an element of the set.
There should be only one of each member (all members are unique).
set Notation
There is a fairly simple notation for sets. We simply list each element, separated by a comma, and then put some curly brackets around the whole thing.
The curly brackets { } are sometimes called "set brackets" or "braces".
Examples of set notation
This is the notation for two examples:
{socks, shoes, watches, shirts, ...}
{index, middle, ring, pinky}
The three dots ... are called an ellipsis, and mean "continue on".
Subset
When we define a set, if we take pieces of that set, we can form what is called a subset.
So for example, we have the set {1, 2, 3, 4, 5}. A subset of this is {1, 2, 3}. Another subset is {3, 4} or even another, {1}. However, {1, 6} is not a subset, since
Empty (or Null) Set
As an example, think of the set of piano keys on a guitar.
"But wait!" you say, "There are no piano keys on a guitar!"
And right you are. It is a set with no elements.
This is known as the Empty Set (or Null Set).There aren't any elements in it. Not one.
Element number
Each item in a set is called the element of the set or the member of the set. The symbol is � eg. {a,e,I,o,u} �=a
Finite sets
It is possible to count the elements in a finite set
Infinite set
It is not possible to count the number of elements that set eg set of even numbers
Universal set
The set from which all the elements are taken. The universal set is denoted by the symbol U
Equal sets
Two sets A and B are equal if they have the same elements, that is, every element which belongs to A also belongs to B, and every element which belongs to B also belongs to A eg A{even numbers less than 10} ={2,4,6,8} B{ multiples of 2 less than 10} = {2,
Equivalent sets
When two sets have the same number of elements, that is n(A)= n(B), we say they are equivalent. Eg A={1,2,3,4,5} B={A,B,C,D,E}
n(A)= n(B)
Compliment
The compliment of a set A is the set of all element in the universal that's not in A. Denoted by A`
Intersection of two sets
The elements common to both A and B for two sets A, B represents the intersection of two sets. Denoted A n B
Union of sets
The elements that are either A or B. Denoted A U B