Materi BAB 1 SMP HIMPUNAN, BILANGAN, DAN OPERASI ALJABAR

<div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 18.2000007629395px; margin: 0px; padding: 0px; vertical-align: baseline;"> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border-image-outset: initial; border-image-repeat: initial; border-image-slice: initial; border-image-source: initial; border-image-width: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">BAB I </span><span style="background-color: white; font-family: inherit; text-align: center;">HIMPUNAN, BILANGAN, DAN OPERASI ALJABAR</span></div> </div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px; text-align: justify; vertical-align: baseline;"> <strong style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; margin: 0px; padding: 0px; vertical-align: baseline;"><span style="background-color: white; font-family: inherit;">I. Himpunan</span></strong></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">Himpunan adalah kumpulan benda-benda dan unsur-unsur yang telah didefinisikan dengan jelas dan juga memiliki sifat keterikatan tertentu.</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px; text-align: justify; vertical-align: baseline;"> <strong style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; margin: 0px; padding: 0px; vertical-align: baseline;"><span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; margin: 0px; padding: 0px; text-decoration: underline; vertical-align: baseline;"><span style="font-family: inherit;">Macam-macam himpunan</span></span></strong></div> <ol style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 18.2000007629395px; list-style: none; margin: 0px 0px 22px 25px; padding: 0px; vertical-align: baseline;"> <li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; list-style: decimal; margin: 0px; padding: 0px; text-align: justify; vertical-align: baseline;"><span style="background-color: white; font-family: inherit;">Himpunan berhingga ® himpunan yang jumlah anggotanya bisa dihitung.</span></li> </ol> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">Contoh :     A = { bilangan prima kurang dari 10}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">                    = {2, 3, 7, 11}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 30px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">   2. Himpunan tak berhingga adalah himpunan yang jumlah anggotanya tidak bisa dihitung atau tidak terbatas.</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">Contoh :  B = { bilangan asli }</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 90px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">           = {1, 2, 3, 4, 5, …}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">          3. Himpunan kosong adalah himpunan yang tidak memiliki anggota.</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">Contoh :     C = { bilangan asli negatif</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 30px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">                                    = { } = Æ                                                                                                                                      4. Himpunan semesta adalah himpunan dari semua obyek yang sedang dibicarakan. Himpunan semesta ditulis dengan simbol S.</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 30px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;"> Contoh :</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 120px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">     D = {1, 3, 5}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 120px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">     Maka himpunan semestanya bisa berupa :</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 120px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">     S = { bilangan asli}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 120px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">     S = { bilangan ganjil }, dan sebagainya.</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 120px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">Î = elemen / anggota / unsur himpunan</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 120px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">Contoh :</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 120px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">A = {1, 2, 3, 4, 5}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 120px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">1 Î A, 3 Î A,  dsb.</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px; text-align: justify; vertical-align: baseline;"> <strong style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; margin: 0px; padding: 0px; vertical-align: baseline;"><span style="background-attachment: initial; background-clip: initial; background-color: white; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; margin: 0px; padding: 0px; text-decoration: underline; vertical-align: baseline;"><span style="font-family: inherit;">Operasi pada himpunan</span></span></strong></div> <ol style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 18.2000007629395px; list-style: none; margin: 0px 0px 22px 25px; padding: 0px; vertical-align: baseline;"> <li style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; list-style: decimal; margin: 0px; padding: 0px; text-align: justify; vertical-align: baseline;"><span style="background-color: white; font-family: inherit;">Komplemen</span></li> </ol> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">A<span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; height: 0px; line-height: 1; margin: 0px; padding: 0px; position: relative; vertical-align: baseline;">c</span> = A komplemen</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">(A<span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; height: 0px; line-height: 1; margin: 0px; padding: 0px; position: relative; vertical-align: baseline;">c</span>)<span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; height: 0px; line-height: 1; margin: 0px; padding: 0px; position: relative; vertical-align: baseline;">c</span> = A         ((A<span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; height: 0px; line-height: 1; margin: 0px; padding: 0px; position: relative; vertical-align: baseline;">c</span>)<span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; height: 0px; line-height: 1; margin: 0px; padding: 0px; position: relative; vertical-align: baseline;">c</span>)<span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; height: 0px; line-height: 1; margin: 0px; padding: 0px; position: relative; vertical-align: baseline;">c</span> = A<span style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; height: 0px; line-height: 1; margin: 0px; padding: 0px; position: relative; vertical-align: baseline;">c</span></span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">2. Irisan</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">       Contoh :</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">       A = {1,2,3,4,5}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">       B = {2,3,5,7,9}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">       A Ç B = {2,3,5}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 30px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">3. Gabungan</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">      Contoh :</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">      A = {2,4,6}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">      B = {4,6,8}</span></div> <div style="background-attachment: initial; background-clip: initial; background-image: initial; background-origin: initial; background-position: initial; background-repeat: initial; background-size: initial; border: 0px; line-height: 20px; margin-bottom: 20px; padding: 0px 0px 0px 60px; text-align: justify; vertical-align: baseline;"> <span style="background-color: white; font-family: inherit;">      A È B = {2,4,6,8}</span></div>

BAB I  HIMPUNAN, BILANGAN, DAN OPERASI ALJABAR I. Himpunan Himpunan adalah kumpulan benda-benda dan unsur-unsur yang telah didefinisi...