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Transcript
Chapter 1: Set Notation
1.
Math 3201
Handout #1
Set
a collection of distinguishable objects
the set notation symbol is brackets { }; not square [ ] or round ( )
sets are equal if they contain the exact same elements even if they are in
different orders
a finite set is one which has a countable number of elements. Ex the set
of integers between 0 and 20
an infinite set is one that has an infinite number of elements. Ex the set
of real numbers
sets can represented by: (i) using words or a sentence; (ii) listing the
elements; (iii) using set notation
ex. {the whole numbers less than 10}; {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
{x / x  10, x W }
2.
Element
each object in a set
the set notation symbol for "is an element of" is ∈
ex. 2 is an element of the set of whole numbers: 2 ∈ 𝑊
3.
Number of Elements
the number of objects in a set
denoted by 𝑛(𝐴)
ex. If A = {2, 4, 6, 8, 10, 12} then 𝑛(𝐴) = 6
4.
Universal Set
the set of ALL elements under consideration for a particular context.
Also called a sample space
5.
Subset
a set whose elements all belong to another set
the set notation symbol for subset is 
ex. Odd whole numbers is a sub-set of whole numbers: O  W
6.
Complement
all elements of a universal set that do not belong to a given subset
the set notation symbol for a complement is the set name and the prime
symbol ‘. In general if A represents a sub-set then A’ represents the
complement
the sum of the number of elements in a set and its complement equals
the universal set 𝑛(𝐴) + 𝑛(𝐴′ ) = 𝑛(𝑈)
ex. If O is the set of odd whole numbers then O’ = {0, 2, 4, 6, 8, …}
Page 1 of 2
Chapter 1: Set Notation
7.
Math 3201
Handout #1
Empty Set
a set with no elements
the set notation symbol for empty set is { }
ex. the set of odd numbers divisible by 2 is an empty set
8.
Disjoint Sets
two or more sets that have no elements in common
ex. the set of even numbers and the set of odd numbers are disjoint sets
“events” that describe disjoint sets are called “mutually exclusive”
(these terms will be used the probability unit)
9.
Venn Diagram
a way of picturing relationships between different groups of things
(sets/subsets)
Named for the person who created it...John Venn
universal set: rectangle ; represents everything in context of the
problem
sub-sets: circles inside the rectangle
each element in the universal set occurs only once.
if an element occurs in more than one subset then it is shown in overlapping subsets. These sections show elements that subsets have in
common; called the “intersection” of two sets. (Section 1.2)
We will work with 2-set and 3-set Venn diagrams in this course
The diagram below to the left is a 2-set Venn diagram
Two Set Venn Diagram
Three Set Venn Diagram
The diagram above to the right is a 3-set Venn diagram
When a Venn diagram shows disjoint sets, the circles do not overlap
Two Set Venn Diagram (Disjoint Sets)
Page 2 of 2