INSTITUT PERGURUAN PEREMPUAN MELAYU MELAKA COURSEWORK MATHEMATICS 1 (SETS) NAME : SYARAFINA BT MOHD SALIM IDENTITY CARD NUMBER : 900917-06-5660 GROUP/COURSE : PPISMP MATHEMATICS JULY 2009 CODE & SUBJECT : MATHEMATICS 1 NAME : NORJAMILAH BT AB.RAHMAN IDENTITY CARD NUMBER : 910902-11-5070 GROUP/COURSE : PPISMP MATHEMATICS JULY 2009 CODE & SUBJECT : MATHEMATICS 1 NAME : HAZIRAH BT MOHD ABDUL WAHID
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INSTITUT PERGURUAN PEREMPUAN MELAYU MELAKA
COURSEWORK MATHEMATICS 1 (SETS)
NAME : SYARAFINA BT MOHD SALIM
IDENTITY CARD NUMBER : 900917-06-5660
GROUP/COURSE : PPISMP MATHEMATICS JULY 2009
CODE & SUBJECT : MATHEMATICS 1
NAME : NORJAMILAH BT AB.RAHMAN
IDENTITY CARD NUMBER : 910902-11-5070
GROUP/COURSE : PPISMP MATHEMATICS JULY 2009
CODE & SUBJECT : MATHEMATICS 1
NAME : HAZIRAH BT MOHD ABDUL WAHID
IDENTITY CARD NUMBER : 910721-11-5338
GROUP/COURSE : PPISMP MATHEMATICS JULY 2009
CODE & SUBJECT : MATHEMATICS 1
Coursework mathematics 1, semester 1,2009
BORANG REKOD KOLABORASI KERJA KURSUS
NAMA PELAJAR : 1) NORJAMILAH BT AB. RAHMAN
NO MATRIK :
KUMPULAN : PPISMP AMBILAN JULAI 2009
SEMESTER : 1
MATA PELAJARAN : MATEMATIK 1
PENSYARAH : PUAN NG PEK FOONG
TARIKH PERKARA YANG DIBINCANGKAN
KOMEN TANDATANGAN PENSYARAH
21/07/2009 Tugasan diberikan beserta penerangan oleh pensyarah
23/07/2009 Pembahagian dan pembentukan kumpulan
Ahli kumpulan terdiri daripada Jamilah, Hazirah, dan Syarafina
30/07/2009 Penerangan kriteria tugasan beserta soal jawab berkaitan pelaksanaan tugasan
30/07/2009 Mengadakan perbincangan kumpulan bagi memahami dengan sepenuhnya kehendak tugasan
Tugasan di bahagikan kepada setiap ahli kumpulan
31/07/2009 Mencari bahan mengikut kehendak tugasan bersama ahli
Nota ringkas dilakukan
2
Coursework mathematics 1, semester 1,2009
kumpulan daripada bahan rujukan di perpustakaan
1/08/2009 dan 2/08/2009
Sambung mencari bahan daripada sumber internet.
4/08/2009 Perbincangan antara ahli kumpulan tentang bahan yang dikumpulkan.
Memastikan bahan yang dikumpulkan memenuhi kehendak tugasan
6/08/2009 Penyemakan sumber oleh pensyarah
8/08/2009 Membincang dan memahami isi-isi bahan yang dikumpulkan bersama ahli kumpulan
10/08/2009 Mencari isi penting di dalam bahan dan membuat rumusan
Nota ringkas dilakukan
11/08/2009 Menyambung membuat rumusan tentang tajuk yang diberikan
12/08/2009 Perbincangan antara ahli kumpulan bagi melengkapkan lagi kerja kursus
Bertukar-tukar pendapat tentang kerja kursus bagi memastikan kerja kursus siap dengan sempurna.
14/08/2009 Penyemakan terakhir tentang kerja kursus dilakukan.
17/08/2009 Tugasan dicetak dan dibukukan dengan
3
Coursework mathematics 1, semester 1,2009
sempurna
19/08/2009 Menghantar tugasan yang telah lengkap kepada pensyarah pembimbing
Penerimaan tugasan oleh pensyarah.
4
Coursework mathematics 1, semester 1,2009
BORANG REKOD KOLABORASI KERJA KURSUS
NAMA PELAJAR : 1) SYARAFINA BT MOHD SALIM
NO MATRIK :
KUMPULAN : PPISMP AMBILAN JULAI 2009
SEMESTER : 1
MATA PELAJARAN : MATEMATIK 1
PENSYARAH : PUAN NG PEK FOONG
TARIKH PERKARA YANG DIBINCANGKAN
KOMEN TANDATANGAN PENSYARAH
21/07/2009 Tugasan diberikan beserta penerangan oleh pensyarah
23/07/2009 Pembahagian dan pembentukan kumpulan
Ahli kumpulan terdiri daripada Jamilah, Hazirah, dan Syarafina
30/07/2009 Penerangan kriteria tugasan beserta soal jawab berkaitan pelaksanaan tugasan
30/07/2009 Mengadakan perbincangan kumpulan bagi memahami dengan sepenuhnya kehendak tugasan
Tugasan di bahagikan kepada setiap ahli kumpulan
31/07/2009 Mencari bahan mengikut kehendak tugasan bersama ahli kumpulan daripada
Nota ringkas dilakukan
5
Coursework mathematics 1, semester 1,2009
bahan rujukan di perpustakaan
1/08/2009 dan 2/08/2009
Sambung mencari bahan daripada sumber internet.
4/08/2009 Perbincangan antara ahli kumpulan tentang bahan yang dikumpulkan.
Memastikan bahan yang dikumpulkan memenuhi kehendak tugasan
6/08/2009 Penyemakan sumber oleh pensyarah
8/08/2009 Membincang dan memahami isi-isi bahan yang dikumpulkan bersama ahli kumpulan
10/08/2009 Mencari isi penting di dalam bahan dan membuat rumusan
Nota ringkas dilakukan
11/08/2009 Menyambung membuat rumusan tentang tajuk yang diberikan
12/08/2009 Perbincangan antara ahli kumpulan bagi melengkapkan lagi kerja kursus
Bertukar-tukar pendapat tentang kerja kursus bagi memastikan kerja kursus siap dengan sempurna.
14/08/2009 Penyemakan terakhir tentang kerja kursus dilakukan.
17/08/2009 Tugasan dicetak dan dibukukan dengan sempurna
6
Coursework mathematics 1, semester 1,2009
19/08/2009 Menghantar tugasan yang telah lengkap kepada pensyarah pembimbing
Penerimaan tugasan oleh pensyarah.
7
Coursework mathematics 1, semester 1,2009
BORANG REKOD KOLABORASI KERJA KURSUS
NAMA PELAJAR : 1) HAZIRAH BT MOHD ABDUL WAHID
NO MATRIK :
KUMPULAN : PPISMP AMBILAN JULAI 2009
SEMESTER : 1
MATA PELAJARAN : MATEMATIK 1
PENSYARAH : PUAN NG PEK FOONG
TARIKH PERKARA YANG DIBINCANGKAN
KOMEN TANDATANGAN PENSYARAH
21/07/2009 Tugasan diberikan beserta penerangan oleh pensyarah
23/07/2009 Pembahagian dan pembentukan kumpulan
Ahli kumpulan terdiri daripada Jamilah, Hazirah, dan Syarafina
30/07/2009 Penerangan kriteria tugasan beserta soal jawab berkaitan pelaksanaan tugasan
30/07/2009 Mengadakan perbincangan kumpulan bagi memahami dengan sepenuhnya kehendak tugasan
Tugasan di bahagikan kepada setiap ahli kumpulan
31/07/2009 Mencari bahan mengikut kehendak tugasan bersama ahli kumpulan daripada bahan rujukan di
Nota ringkas dilakukan
8
Coursework mathematics 1, semester 1,2009
perpustakaan
1/08/2009 dan 2/08/2009
Sambung mencari bahan daripada sumber internet.
4/08/2009 Perbincangan antara ahli kumpulan tentang bahan yang dikumpulkan.
Memastikan bahan yang dikumpulkan memenuhi kehendak tugasan
6/08/2009 Penyemakan sumber oleh pensyarah
8/08/2009 Membincang dan memahami isi-isi bahan yang dikumpulkan bersama ahli kumpulan
10/08/2009 Mencari isi penting di dalam bahan dan membuat rumusan
Nota ringkas dilakukan
11/08/2009 Menyambung membuat rumusan tentang tajuk yang diberikan
12/08/2009 Perbincangan antara ahli kumpulan bagi melengkapkan lagi kerja kursus
Bertukar-tukar pendapat tentang kerja kursus bagi memastikan kerja kursus siap dengan sempurna.
14/08/2009 Penyemakan terakhir tentang kerja kursus dilakukan.
17/08/2009 Tugasan dicetak dan dibukukan dengan sempurna
9
Coursework mathematics 1, semester 1,2009
19/08/2009 Menghantar tugasan yang telah lengkap kepada pensyarah pembimbing
Penerimaan tugasan oleh pensyarah.
10
Coursework mathematics 1, semester 1,2009
REFLECTION
By : Norjamilah Bt Ab. Rahman
On 21th July 2009, we are given a short course work about “ set ” from our
dedicated lecture, Madam Ng Pek Foong. She gave an excellent explanation to
us how to do this short course work so that this short course work will successful
finished. She divided the students into six groups which contains three member
in each group. We are given three weeks to finish and submit this short cour se
work on 19th August 2009.
According to the explanation given by our lecture, we are supposed to find
out what is the set. We have to do a research about set from many aspects. The
aspects are including history of set, set theory or set concepts and application of
set in our daily life. We try to find as many as possible about what is set through
many ways.
Then, in our group, we discuss how to do this short course work properly.
Based on a good commitment and cooperation giving by all members in our
group, we managed to plan and divided a task to each members in our group.
Through this short course work, we can refresh what we have learnt when
we was in the secondary school. Based on the experiences, we do a research
about set through many resources likes various types of books and a lots of
information from internet.
During finishing this short course work, we were confronted by a little
problem. We have to managed our time properly between study and doing this
short course work. But, thanks to God because of our commitment to our work,
we are finally can overcome this problem.
Then, while doing this short course work, we know our weakness and our
strength about set. After doing a research, we found a lot of information about set
that we do not know before this. So, by doing this short course work, we can gain 11
Coursework mathematics 1, semester 1,2009
our knowledge. From the research, we found that set give a big implication in our
daily life.
Finally, after having a had struggle doing this short course work, we are
success to finish it completely. We hope that through this short course work, we
can gain our knowledge about set especially about its history, theory or concepts
and application to our daily life.
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Coursework mathematics 1, semester 1,2009
By : Hazirah Binti Mohd Abdul Wahid
On 21st July 2009, I was given a task on a short coursework about set by my
Mathematics lecturer, Ms. Ng Pek Foong. This task should be done in a group of three
members and submit it on 19th August 2009.We were asked to collect information from
books, journals, and internet about history, theory and application about sets.
After the task was briefing by Ms. Ng Pek Foong, I started to find my group
members. Finally, Syarafina and Jamilah and I decided to become a group and we
agree to take Jamilah as our group leader who will responsible in assigning the tasks
and held group discussion.
Then, we held a group discussion and began to divide the works fairly to each of
the group’s member, I was asked to gather information on application of sets and make
reviews on that topic. Actually, this is my first experience on making a coursework. So,
I’m quite nervous and blur on how to make an excellent and impressive coursework. My
group and I decided to ask everything about this task that we don’t know to Ms. Ng Pek
Foong and she gave a good explanation about the task which helps us a lot.
After that, we started to collect information as many as we can about sets. My
group’s member and I went to the library and it’s a relief that we had found a lot of
books and journals about sets at the library. We collected all of them, photostat, and
made a review. Even, I had to use a lot of money in order to copy the information but it
is worth for me because I want to give the best commitment as I can to this task.
However, we know that there must be a great challenge in making a good thing. In
my case, my group’s member and I had a difficulty in finding information on the internet
because there is no wireless connection in the hostel except at the library.
We had to find it on the computer at the library and save it on the pen drive. This
way is quite hard as the wireless connection is really slow and the computer that is
provided is in a small amount and many students want to use too. Finally we found the 13
Coursework mathematics 1, semester 1,2009
solution to this problem and agree to borrow the broadband from the senior to find the
information.
For this problem, I want to suggest the institute to provided the wireless connection
at the hostels as we know that internet is really important for the students to find
information about a lot of thins in order to make it easier for us to do our assignment.
Besides, my group and I also had a problem in managing our time well. There are
a lot of jobs to do and we had to steal sleeping time to finish this coursework. However,
we got a great learning from this experience that is we have to make a timetable from
the beginning to make sure our jobs are done smoothly.
Although, I had to sacrifice my time for rest and sleep, my money and my energy to
complete this task it is worth when eventually I managed to accomplish my goal of
finishing this works. One of the reasons is because I had works with such an amazing
persons, my group members, Syarafina and Jamilah who are ready to give the best
cooperation and go through all of the problems in making this task together with me.
Moreover, I had learnt a lot from my experience in making this task such as we
have to be patient and try to find the solutions when the problems come rather than
make it as an excuse for us. We must also give our best and our commitment when do
a thing so that we will satisfied with our jobs at the end.
14
Coursework mathematics 1, semester 1,2009
By : Syarafina Binti Mohd Salim
Thanks to God, after 1month finally, my group and I had finish completely our
mathematic 1 coursework. Since this is my first coursework, I found many problem,
our weakness and also strength during doing it.
First and foremost my group and I faced a little problem when searching and
collect data about the title, sets especially the history of sets. Actually, it is easy to find
the information about sets. Maybe because this is famous and popular topic . the
problem happen when we didn’t focus to the subtopic. However, our senior had help
us a lot. They had show us the actual way in finding data.
After we had collected data, we cant make a review properly because our data is
included somethings which is not important. Fortunately ,our lecturer, madam Ng Pek
Foong had teach us a lot.
Besides that, I found that my group didn’t organized and planned when and how
to do the work properly. We do it suddenly and without plan first. Sometimes it is quit
messy. We also didn’t divide work among the group members. This make some of us
work harder and some also do it but only a little. Finally, we had done the coursework
but only at the last minute.
From the problem I had identified above, I learned that if we get another
coursework in the future, we must plan it first. We also must choose one leader in our
group to make sure the work is always done and to divide work fairly. Even this is a
group work, we should divide work to ensure all members contribute their ideas, times
and energy to get a quality coursework.
Absolutely there is not only the problem and weaknesses I found when spending
my time to do this coursework. I noticed that is a lot of benefits and strength in it. One
of them is I had improved my knowledge about sets. My friends and I had do research
about sets. It is quit exciting because there is a lot of things we don’t know before. For
15
Coursework mathematics 1, semester 1,2009
example, we had knew about the history of Geog Cantor, a famous mathematician
which we didn’t ever heard his name before.
The most sweet things is my relationship between me and my group had
become closer because we had spent many time together to discuss about our
coursework. We also had ask a lot question to our lecturer, madam Ng Pek Foong.
This is due to our misunderstanding about the real way to do this coursework. I know
that this is very important so I don’t want we do it completely but wrongly.
Furthermore, because of this coursework I learned that how cooperation is very
important in a group. I also learned how to communicate with teamwork and be
rational. We must discuss between our members to achieve agreement when decide
something.
In conclusion, I found that this coursework is good and I am pleasure to do
another coursework in the future. Thank you.
16
Coursework mathematics 1, semester 1,2009
HALAMAN PENGAKUAN“ Saya akui karya ini adalah hasil kerja saya sendiri kecuali nukilan dan ringkasan yang
tiap-tiap satunya telah saya jelaskan sumbernya”
Tandatangan :
Nama penulis: NORJAMILAH BT AB RAHMAN
Tarikh : 18/08/2009
“ Saya akui karya ini adalah hasil kerja saya sendiri kecuali nukilan dan ringkasan yang tiap-tiap satunya telah saya jelaskan sumbernya”
Tandatangan :
Nama penulis: SYARAFINA BT MOHD SALIM
Tarikh : 18/08/2009
“ Saya akui karya ini adalah hasil kerja saya sendiri kecuali nukilan dan ringkasan yang tiap-tiap satunya telah saya jelaskan sumbernya”
Tandatangan :
Nama penulis: HAZIRAH BT ABDUL WAHID
Tarikh : 18/08/2009
17
Coursework mathematics 1, semester 1,2009
CONTENTS
CONTENTS PAGE
INTRODUCTION
ACKNOWLEDGEMENT
REVIEW
TOPICS
HISTORY OF SETS
THEORY OF SETS :
-CONCEPT OF SETS
-SUBSETS, UNIVERSAL SETS, AND
COMPLEMENT OF SETS
-OPERATIONS OF SETS
APPLICATION OF SETS
CONCLUSION
BIBILOGRAPHY
18
Coursework mathematics 1, semester 1,2009
INTRODUCTION
The human mind likes to create collections. Instead of seeing a group of five
stars as five separate items, people tend to see them as one group of stars. The mind
tries to find order and patterns. In mathematics this tendency to create collections is
represented with the idea of a set. A set is a collection of objects. The objects
belonging to the set are called the elements or members of the set.
An example of a set is the set is the set of the days of the week, whose elements
are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday.
Capital letters are generally used to name sets. Lets use W to represent the set
of the days of the week.
Three methods are commonly used to designated a set. One method is a word
description. We can describe set W as set of the days of the week. A second method is
the roster method. This involves listing the elements of a set inside a pair of braces, { }.
The braces at the beginning and end indicate that we are representing a set. The roster
form uses commas to separate the elements of the set. Thus, we can designated the