Operasi Himpunan

>> Operasi Himpunan

• Gabungan (Union) : U
• Irisan (Intersection) : n
• Pelengkap (Complement) : A’
• Selisih : A – B

>> Diagram Venn

• Gabungan : A U B

• Irisan : A n B

• Pelengkap : A’

• Selisih : A – B

>> Contoh Soal

U = {1,2,3,4,5,6,7,8,9}
P = {1,2,3,4,5}
Q = {4,5,6,7,8}
R = {6,7,8,9}
Maka:

• P U Q = {1,2,3,4,5,6,7,8}
• P U R = {1,2,3,4,5,6,7,8,9}
• Q U R = {4,5,6,7,8,9}
• P n Q = {4,5}
• P n R = {} = Ø
• Q n R = {6,7,8}
• P – Q = {1,2,3}
• P – R = {1,2,3,4,5}
• Q – R = {4,5}
• U – P = {6,7,8,9} --> P’
• U – Q = {1,2,3,,9} --> Q’
• U – R = {1,2,3,4,5,} --> R’

>> Coba Latihan Lagi

Soal No 1
U = {1,2,3,4,5,6,7,8}
A = {2,3,5,7}
B = {1,3,4,7,8}
Maka :

• A’ = {1,4,6,8}
• B’ = {2,5,6}
• A – B = {2,5}
• B – A = {1,4,8}
• A n B = {3,7}
• A U B = {1,2,3,4,5,7,8}
• B n A’ = {1,4,8}
• A n B’ = {2,5}

• 
  

Soal No 2

U = {x; 3 <- x < 14}
A = {6,7,9,10,13}
B = {4,5,11}

Maka :

A’ = {3,4,5,8,11,12}
B’ = {3,6,7,8,9,10,12,13}

• A – B = {6,7,9,10,13}
• B – A = {4,5,11}
• A U B = {4,5,6,7,9,10,11,13}
• A U B’ = {3,6,7,8,9,10,12,13}
• A n B = {} = Ø

Materi Kuliah Matematika Kalkulus
Jum'at, 20 Nopember 2009