Set
A collection of objects whose content can be clearly determined
Elements , Members
Objects in a set
Sets
Can be designated by word description , the rooster method , or set-builder notation
Empty set or Null set
Is represented by {} or o/ = a set that contains no elements
E
Means the object is an element of the set
E/
Means the element is not an element of the set
Set of Natural Numbers
N={1,2,3,4,5,...}
x<a
x is less than a = Inequality Notation
The Cardinal Number of a Set A
n(A), is the number of distinct elements in a set A ( Repeating numbers of the set neither adds new elements to the set nor changes the cardinality
Equivalent Sets
Have the same number of elements , or the same cardinality
One-to-One Correspondence between set A & Set B
Means that each element in A can be paired with exactly one element in B, and vise versa
If two sets can be placed in a One-to-One Correspondence
then they are equivalent
Set A is a finite set if
n(A)=0
A set that is not finite is
Infinite set
Equal Sets
Have the same elements , regardless of order or possible repetition of elements
Equivalent
If two sets are equal they must be equivalent
Subset
Set A is a ____ of Set B ,if every element in set A is also in Set B (expressed as A c B )
A /C B
Means that set A is not a subset of set B so There is one element in set A that is not in set B
Set A is the Proper Subset of set B
If every A is a subset of B and A=/B ( expressed as ACB
An empty set
Is a subset of every set
A set with n elements has
A subset 2n distinct subsets & 2n-1 distinct proper set
Universal set
Is a set that contains all the elements being considered in a given discussion or problem ( symbolized by U )
Venn Diagrams
Represent two Subsets of a universal set
A' ( the complement of set A) which can be read A prime or not A
Is the set of all elements in the universal set that are not in A
A u B ( A intersection B ) which can be read set A and set B
Is the set of elements common to both set A and set B
AUB ( A union B) , which is read set A or set B
Is the set of elements that are members of set A or of set B or both sets
Some problems involve more than one set operation
Begin b preforming any operation inside the parentheses
Venn Diagram
Elements of sets involving a variety of sets operation can be determined by using
Cardinal numbers of the union of two finite sets
n(A U B)= n(A) t n(B) - n( A u B )
Operation within Parentheses
When using set operations involving three sets , begin by preforming _____
Three intersecting sets
Separate the universal set U , into eight regions
Ductively proves two sets are equal
If two specific sets represent the same regions of a venn diagram then this ________
And & But ,,, Or ,,,, Not
Venn Diagrams can be used to organize information collected in surveys. when interpreting cardinalities in such diagrams ___,___ means intersection , _ means union and - __ means complement
To Solve a Survey Problem
1. Define sets and draw a Venn Diagram
2. Fill in the cardinality of each region , starting with the innermost region and working outward
3. Use the completed diagram to answer the problems question