Selasa, 13 Mei 2014

Latihan Soal Materi Himpunan

Latihan 1

1. a. Berilah tiga contoh kumpulan yang bukan merupakan himpunan.
    b. Berilah tiga contoh kumpulan yang merupakan himpunan.

2. Diketahui B = {p, q, r}. Katakanlah apakah keempat pernyataan berikut benar,
kemudian berikan alasannya.
 a. p   B
b. {q}   B,
c. r   B,
d. s   B.

3. Tulislah himpunan berikut dengan tabulasi.
a. A = {x^2 = 25}
b. B = {x| x + 3 = 3}
c. A = {x| x > 3, x bilangan asli ganjil}
d. A = {x| 0 < x < 5, x bilangan real}

4. Tulislah dengan menyebutkan syarat-syarat anggotanya.
a. E = {a,i,u,e,o}
b. F = {2,3,5,7,11}
c. G = {3,6,9,12, …}
d. H = {123, 132, 213, 231, 312, 321}.

5. Tulislah dengan notasi pembentuk himpunan untuk himpunan bilangan asli yang:
a. kurang dari 5,
b. Iebih dari atau sama dengan 3,
c. kelipatan 5 kurang dari 50, dan
d. prima.

6. Penulisan himpunan berikut manakah yang benar
a. J= {x| x > 0, x   himpunan bilangan bulat}
b. K = {x| x < 20, x bilangan asli genap}
c. L = {x| x > 4, x bilangan cacah}

 Jawab :

1.   a. Kumpulan yang bukan merupakan Himpunan
  •  Kumpulan cowok-cowok ganteng
  •  Kumpulan orang pintar
  • Kumpulan wanita cantik
      b. Kumpulan yang merupakan Himpunan

  • Kumpulan hewan berkaki dua
  •  Kumpulan cewek berhijab di kampus
  • Kumpulan kendaraan beroda dua
2.  a.  p ϵ B  

          jawab : benar, karena p merupakan anggota himpunan B

     b. {q} ϵ B
          jawab : salah,

     c.  r ϵ B 
          jawab : benar, karena r merupakan anggota himpunan B

     d. s ϵ B 
         jawab : salah, karena s bukan merupakan anggota himpunan B

3.  a.   A = {x2 = 25}
            Jawab : A = {5}

     b.   B = {x| x + 3 = 3}

                 Jawab : B = {0}

    c. A = {x| x > 3, x bilangan asli ganjil}
                Jawab : A = {5, 7, 9, 11, 13, …}

    d. A = {x| 0 < x < 5, x bilangan real}
               Jawab : A = {…   …}
4.  a. E = {a,i,u,e,o}  
                Jawab : E himpunan huruf vocal

     b. F = {2,3,5,7,11}
               Jawab : F himpunan bilangan prima

     c. G = {3,6,9,12, …} 
                Jawab : G himpunan bilangan perkalian 3

     d. H = {123, 132, 213, 231, 312, 321}. 
               Jawab : H himpunan bilangan ... 
5. a. kurang dari 5,
    Jawab : A = {x| x < 5, x bilangan asli}

    b. Iebih dari atau sama dengan 3,

         Jawab : B ={x| x ≥ 3, x bilangan asli}
    c. kelipatan 5 kurang dari 50, dan
         Jawab : C = { x| x kelipatan 5 kurang dari 50}

   d. prima. 
         Jawab : D = { x | x bilangan prima }
6.  a. J= {x| x > 0, x ϵ himpunan bilangan bulat}
        Jawab : Salah

     b. K = {x| x < 20, x bilangan asli genap}
               Jawab : Benar

     c. L = {x| x > 4, x bilangan cacah} 
              Jawab : Benar 
(Sumber : Buku Bahan Ajar Pengantar Dasar Matematika oleh Haris Kolengsusu, S.Pd, M.Cs)


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