Himpunan dalam Matematika Disktrit, Definisi dari himpunan sendiri adalah kumpulan objek yang berbeda; kumpulan objek yang didefinisikan dengan jelas (well defined); kumpulan objek yang mempunyai syarat tertentu dan jelas. Contoh Himpunan bilangan 1, 3, 5, 7, 9.
Objek di dalam himpunan disebut elemen,unsur,atau anggota. HMPSSI (Himpunan Mahasiswa Program Studi Sistem Informasi) FTI UMBY adalah contoh sebuah himpunan yang di dalamnya berisi anggota berupa mahasiswa. Tiap mahasiswa berbeda satu sama lain.
Perbedaan:
- {1, 2, 3, 4, 5, 6 } Himpunan (set)
- {1, 2, 2, 3, 4, 4, 4, 5, 6} Bukan himpunan tetapi Himpunan-ganda (multi-set).
Cara Penyajian Himpunan dengan Enumerasi setiap anggota himpunan didaftarkan secara rinci.
Contoh 1.
- Himpunan empat bilangan asli pertama: A= {1, 2, 3, 4}.
- Himpunan lima bilangan genap positif pertama: B= {4, 6, 8, 10}.
- C={kucing,a,Amir,10,paku}
- R= { a, b, {a, b, c}, {a, c} }
- C= {a, {a}, {{a}} }
- K= { {} }
- Z = {Laptop, Komputer, Laptop Bisnis, Laptop Pelajar, Laptop Editor}
- B = {RAM, VGA, HDD, SSD}
- Himpunan 100 buah bilangan asli pertama: {1,2,…,100}
- Himpunan bilangan bulat ditulis sebagai {…,-2,-1,0,1,2,…}.
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Berikut adalah beberapa tipe himpunan dan pengertian nya.
Himpunan Semesta
- Himpunan semesta adalah himpunan yang mempunyai anggota semua objek yang dibicarakan
- Himpunan semesta biasanya diberi lambang U (universe) atau S (semesta).
- Contoh : Yang dapat menjadi semesta pembicaraan dari
- A = {1, 2, 3, 4, 5} adalah :
- S = {1, 2, 3, 4, 5, …}= himpunan bilangan asli, atau
- S = {0, 1, 2, 3, 4, 5, …}= himpunan bilangan cacah,
- S = {…, 0, 1, 2, 3, 4, 5, …}= himpunan bilangan bulat.
Himpunan Kosong (null set)
- Sebuah himpunan dikatakan sebagai himpunan kosong bila himpunan tersebut tidak memiliki anggota.
- Himpunan kosong biasanya dilambangkan dengan { } atau Φ.
- Contoh : P = himpunan bilangan prima kelipatan empat
Relasi antara Himpunan
- Himpunan bagian / subset (⊂ )
- Himpunan yang sama (=)
- Himpunan yang berpotongan
- Himpunan saling lepas (||)
- Himpunan ekuivalen (∞)
Operasi Himpunan
- Gabungan / Union (∪)
- Irisan / Intersection (∩)
- Komplemen (‘ / c)
- Selisih dua himpunan / difference (-)
- Jumlah dua himpunan / symetric difference (+)
- Perkalian / cross product (x)
Daftar Pustaka dan bahan Bacaan
- belajarstatistics.com/blog/2021/05/25/dasar-dasar-teori-himpunan/
- Ardanari, Patricia. 2015. Logika Matematika : Teori Himpunan. Yogyakarta: Indonesia Publishing House.
Kontributor : Agustinus Kafiar / FTI UMBY
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