Transcript Set Notations

OTCQ 09/14/09
Define point and plane.
Aim 1-1 part 2
How do we use set and interval
notation, and find a complement of
a set?
NY AA 29 and AA 30
Aim 1-1 Standards (NO
WRITE)
A.A.29 Use set-builder notation
and/or interval notation to illustrate
the elements of a set, given
the elements in roster form
A.A.30 Find the complement of a
subset of a given set, within a given
universe
Aim 1-1 Objectives(Please write)
SWBAT
1.Use { and } to write sets as lists aka rosters
in set builder form.
2.Translate from < and >, < and >, open
circles, closed circles, set interval notation ( )
and[ ].
3.Understand complement means anything not
included in the set but still in the universe.
4.Understand that the universe is everything of
that kind.
OBJ#1 Sets and set notation
A set is a collection of objects called the elements
or members of the set.
Set braces { } may be used to list the elements of a
set.
Example {1,2,3}
Translated {1,2,3} means the set of numbers
including 1, 2 and 3
This is referred to as a Finite Set since we can count
the elements of the set.
Sets and set notation
Example : N= {1,2,3,4,…} is referred to as the
Natural Numbers or Counting Numbers Set.
• Example : W= {0,1,2,3,4,…} is referred to as the
Whole Number Set.
• What does . . . mean?
• Can you recall the other number sets?
• I – Integer numbers: {…,-2, -1, 0, 1, 2, …}
• R - Rational numbers (repeating decimals and
fractions).
• IR – Irrational numbers: (can’t be expressed as
fractions, decimals that never repeat).
• Any questions about set braces { and }?
OBJ 2
First, lets recall how to graph
inequalities on a number line.
Then we will connect this knowledge to
the description of a set of numbers.
Go to:
http://www.phschool.com/atschool/acad
emy123/html/bbapplet_wl-problem430715.html
The number line represented by
x > 5 is a set.
In words x > 5 means the set of all
numbers greater than or equal to 5.
What is the greatest number in that
set?
Would it be convenient to list all the
numbers between { and }?
Next, connecting number lines and set interval
Notation.
Rules for translating from
inequalities to number lines and
then to set interval notation.
1. < and > go with open circles
and ( and ).
2. < and > go with closed circles
and [ and ].
5 < x < 10
For this example think of only
natural numbers!
Ex:
We will
1. Graph this on a number line.
2. Translate this to words that describe a
set.
3. Translate this to set interval notation.
5 < x < 10
Please
1. Graph this on a
number line.
2. Translate this to
words that
describe a set.
3. Translate this to
set interval
notation.
<
5
<
10
Notice that based on
the rules I chose an
open circle for 5 and
a closed circle for 10?
5 < x < 10
Please
1. Graph this on a
number line.
2. Translate this to
words that
describe a set.
3. Translate this to
set interval
notation.
5
10
In words, the number
line describes the set
of numbers greater
than 5 and less than
or equal to 10.
5 < x < 10
Please
1. Graph this on a
number line.
2. Translate this to
words that
describe a set.
3. Translate this to
set interval
notation.
<
<
(
5
]
10
(5,10] = Set Interval
notation.
Notice that < and (
go together and <
and ] go together.
This also means the
numbers greater than
5 and less than or
equal to 10.
5 < x < 10 could als be
listed in braces as
{6,7,8,9,10}
Using only natural
numbers.
Summary so far objs 1 & 2:
 5 < x < 10 can be expressed as a
number line graph.
10
5
 5 < x < 10 can be translated as (5,10].
 5 < x < 10 can be translated as
{6,7,8,9,10}.
You try:
-3 < x < 4
Please (we try together)
1. Graph this on a number line.
2. Translate this to words that describe
a set.
3. Translate this to set interval notation.
One for you:
-3 < x < 4
-3
Please
1. Graph this on a
number line.
2. Translate this to
words that
describe a set.
3. Translate this to
set interval
notation.
4
One for you:
-3 < x < 4
-3
Please
1. Graph this on a
number line.
2. Translate this to
words that
describe a set.
3. Translate this to
set interval
notation.
4
#2: The set of numbers
greater than or
equal to -3 and less
than 4.
One for you:
-3 < x < 4
-3
Please
1. Graph this on a
number line.
2. Translate this to
words that
describe a set.
3. Translate this to
set interval
notation.
4
[-3,4)
How could we write x < -2?
Does < go with ( and ) or [ and ]?
How could we write x < -2
With set interval notation?
< goes with ( and ).
But try a number line first just so
you see what else has to go in
the interval notation.
x < -2?
< goes with ( and ), but the number line
arrow points left which means we are
headed for - . So we write
[-,-2)
In words this means?
Why did I use a bracket for - infinity?
Because the [ implies equal to. Always
use a bracket next to infinity.
How could we write x < -2
with { and }?
{ . . . -5, -4, -3, -2}
This is probably the best for this
example.
We have several ways to describes
sets because we like to choose
the simplest.
OBJ 3
Venn Diagrams, Complements and
Subsets


Set B is called a subset of the set A if all
of Set B (blue area) is contained in Set A
(Green area)
B⊂A
A
B


A
The complement of Set B within Set A means
anything outside of Set B and still within set A.
Can you think of any examples of sets, subsets
and complements? OTCQ Tuesday. Like: What
is the complement of Queens in NYC?
Aim 1-1 Objectives Check back(no write)
SWBAT check. Can you? Let’s look at our
worksheet/homework?
1.Use { and } to write sets as lists aka rosters in
set builder form.
2.Translate from < and >, < and >, open circles,
closed circles, set interval notation ( ) and[ ].
3.Understand complement means anything not
included in the set but still in the universe.
4.Understand that the universe is everything of
that kind.
Xc?


Union
The union of two sets
A and B
is the set of all
elements x such that
x is in A OR x is in B
Notation:
A∪B
A
A∪B
B
Intersection

The intersection
of two sets
A and B
is the set of all
elements x such that
x is in A AND x is in B
B
A
A∩B

Notation:
A∩B