Contemporary Math 120

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