OTCQ 09/14/09

Define point and plane.

Aim 1-1 part 2How 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, giventhe elements in roster formA.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 2First, 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/academy123/html/bbapplet_wl-problem-430715.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 }?

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 ].

Next, connecting number lines and set intervalNotation.

Ex: 5 < x < 10For this example think of only

natural numbers!

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

Please1. 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

Please1. 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

Please1. 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.

5 < x < 10 can be translated as (5,10].

5 < x < 10 can be translated as {6,7,8,9,10}.

5 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

Please1. Graph this on a

number line.2. Translate this to

words that describe a set.

3. Translate this to set interval notation.

-3 4

One for you:

-3 < x < 4

Please1. Graph this on a

number line.2. Translate this to

words that describe a set.

3. Translate this to set interval notation.

-3 4

#2: The set of numbersgreater than or equal to -3 and lessthan 4.

One for you:

-3 < x < 4

Please1. Graph this on a

number line.2. Translate this to

words that describe a set.

3. Translate this to set interval notation.

-3 4

[-3,4)

How could we write x < -2?Does < go with ( and ) or [ and ]?

How could we write x < -2With 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 3Venn 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

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?

B A

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 setsA and Bis the set of allelements x such thatx is in A OR x is in B

Notation:A ∪ B

A B

A ∪ B

Intersection

The intersectionof two setsA and Bis the set of allelements x such thatx is in A AND x is in B

Notation:A ∩ B

A B

A ∩ B