Mathematics DutyMathematics DutyChapter VIChapter VI

SetsSetsCreated By:Created By:

Timotius Ivan. S.Timotius Ivan. S.Danny Agus Pramana. W.Danny Agus Pramana. W.

Dewa Ngurah Yudi. P.Dewa Ngurah Yudi. P.

6.1 Sets and members of a 6.1 Sets and members of a setssets

Venn Diagram

Operation of Sets

Sets

Concept of Sets

Subset

Operation of Setsand Venn Diagram

A Definition

Membership a Sets

Cardinal Number

Subset

Set universe

Intersection

Union

A. The Notion Of A SetA. The Notion Of A Set If you look carefully in a football match, what do If you look carefully in a football match, what do

you see?you see?We can see there are different collection, such as:We can see there are different collection, such as:1.1. Football playersFootball players2.2. The goal keeperThe goal keeper3.3. The ballThe ball4.4. The football referee The football referee 5.5. AudienceAudience6.6. Backup players.Backup players.Its mean the notion of a set is member of one set, Its mean the notion of a set is member of one set,

like the footballplayers in a football team.like the footballplayers in a football team.

B. Elements of A SetB. Elements of A Set

Now we will give you a simple question.Now we will give you a simple question.

Find H if H=(names of days starting with T)Find H if H=(names of days starting with T)

In mathematics, to express In mathematics, to express an element an element of a of a set, the symbol is set, the symbol is ЄЄ(member of). And to (member of). And to express not the element is express not the element is ЄЄ (not a member (not a member of)of)

So H is:So H is: Sunday Sunday ЄЄ H H Monday Monday ЄЄ H H Thursday Thursday ЄЄ H H

Tuesday ЄЄ H

Wednesday ЄЄ H

6.2 Expressing Sets

• Sets is a corps of kinds of objects in one community.

• Expressing sets is the way to write a sets from numbers to words.

We can say the examples:1.There are chairs, whiteboard, and desk

is the materials in class whose make the class community

A. The way of expressing sets• P=(2,3,5,7). If we write it, like: P is a

set of prime number less than ten• Some another examples1. K=(1,3,5,7,9,11):K is a set of odd

number less than twelve.2. L=(January, June, July) :L is a set of

name of month starting with J.3. M=(1,2,3…100):M is a set of natural

numbers from one until one hundred.

B. Acquiring the sets of elements• At primary school, we already learned

several kinds of sets of numbers, such as:

1. C=set of counting numbers C=(0,1,2,3,..)

2. Z=set of odd numbers Z=(1,3,5,..)3. W=set of even numbers/W=(0,2,4,6,..)

6.3 Set Cardinality Cardinal Number is a number to expressing

many members of one members, symbolizing by n, n is the members.

We can say the examples: There are 23 boy (B) pupil and 20 girl (G) pupilSo, we can write it:n(B)=23, n(G)=20, n(U)=43If the question "Is there any pupil which height 3

meters here?” we can answer it with use the empty sets symbol Ø

What is the mean of universe set?

Universe set is the widest of the sets in one case

We can say the examples:

1.What is the universe set of B=(2,4,6,8)

The answer: because B is a even number, so the set universe of B is:

U=(a natural numbers less than ten), so

U=(1,2,3,4,5,6,7,8,9)

Set universe, Relation between two sets and empty set.

Empty set is a member of set ,which don’t have any members and symbolizing with { } or ØThe set universe is a set containing all elements of the set being talked about. The universe set can symbol by U

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Set universe, Relation between two sets and empty set

Relation between two sets suppose:If A=red , yellow B=red, blue C=red, yellow, greenDoes set c contain all set a?Does set c contain all set b?

Because C contains all elements of A, C can be called as” a relation set” of a set ABecause there is an element B not included in C, that is blue, so C is not “a relation set” of B

6.4 the Venn Diagram6.4 the Venn Diagram

Relation between a sets with its universe Relation between a sets with its universe can be modeled with a diagram is called can be modeled with a diagram is called Venn diagram.Venn diagram.

We can say the examples:We can say the examples:

B=(2,4,6,8),S=(1,2,3,4,5,6,7,8,9). The Venn B=(2,4,6,8),S=(1,2,3,4,5,6,7,8,9). The Venn diagram of this question.diagram of this question.

B=0 S=1,3,5,7,92,4,6,8

1,2,3,4,5,6,7,8,9

6.5 Intersection6.5 IntersectionIntersection is sets slice of A and of B is A Intersection is sets slice of A and of B is A sets which its member represent the sets sets which its member represent the sets member A as well as B.member A as well as B.

If A=(a,s,d), B=(a,c,d,r)If A=(a,s,d), B=(a,c,d,r)

Or we can write it with intersection symbolOr we can write it with intersection symbolS

c,r s

AB

a,d

6.6 The Union of Two Sets6.6 The Union of Two Sets

The union of two sets is sets combination The union of two sets is sets combination of A and of B, is sets which its member is of A and of B, is sets which its member is the member of A or member or B.the member of A or member or B.

Or we can write it with union symbol (Or we can write it with union symbol (U)U)

Like A U BLike A U BA

B

6.7 Complement and Set 6.7 Complement and Set DifferenceDifference

FROM ALL MENTIONED STATEMENT WE CANFROM ALL MENTIONED STATEMENT WE CAN

SAY:SAY:Sets is a corps of kinds of objects in one community

Cardinal Number is a number to expressing many members of one memberssymbolizing by n(M), if M is the sets and n is the members.

Sets universe is the widest of the sets in one case

Relation between a sets with its universeRelation between a sets with its universe sets cansets cana diagram is called Venna diagram is called Venn diagram.diagram.

be modeled withbe modeled with

Intersection is sets slice of A and of B is a sets which its member

represent the sets member of A as well as B.The union of two sets is sets combination of A and of B,

sets which its member is the member of A or member or B.Page one

6.7 Complement and 6.7 Complement and Set DifferenceSet Difference Empty set is a member of set ,which don’t have any Empty set is a member of set ,which don’t have any

members and notation with members and notation with { }{ } or or ØØ

Slice set, if a and b is two sets where each member set a is a Slice set, if a and b is two sets where each member set a is a member of set b, so set a is the slice set of set b and member of set b, so set a is the slice set of set b and notation with A notation with A BB

Intersection two sets A and B is a set where its member is Intersection two sets A and B is a set where its member is the member of A and member of Bthe member of A and member of B

The union of two sets A and B is a set where its member is The union of two sets A and B is a set where its member is the member of A and the members of B the member of A and the members of B

A n B=(x x€A or x€B

A U B=(x x€A or x€B

Page two

The Question and The AnswerThe Question and The Answer

1.1. If we see the basketball player, of If we see the basketball player, of course we imagine their height. course we imagine their height. Please write 2 nonempty sets and 2 Please write 2 nonempty sets and 2 empty sets!empty sets!

a.a. Nonempty set:Nonempty set:

b.b. Empty set:Empty set:

1.They are 3m

2.They can including the ball because they are tall

1.They are handsome

2.They are a good basketball team.

The Question and The AnswerThe Question and The Answer

2.A car need gasoline 40 liters for 2.A car need gasoline 40 liters for going through the ways 456km. If going through the ways 456km. If there is a gasoline 60 liters, how far there is a gasoline 60 liters, how far that car can going through the that car can going through the ways?ways?

It can:456/40 x 60=218x3=654kmIt can:456/40 x 60=218x3=654km

The Question and The Answer

3.Seventy two books have weight 9kg. How many that books if their weight is 6kg?

There are:9/6x72=108 books.

THAT ALL ABOUT SETS,THANK YOU FOR YOUR ATTENTION AND HAVE A NICE DAY!!!!!