APENSO INDONESIA

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Dasar - Dasar Matematika (30)

Dasar - Dasar Matematika (30)


Oleh : Suryadi 
Director of Education Apenso Indonesia

Hukum De Morgan
1. ( A ∪ B )’ = A’ ∩ B’
2. (A ∩ B )’ = A’ ∪ B’

Contoh :
A = { 2, 3, 4, 5, 6 }
B = { 4, 5, 6, 7, 8, 9 }
S = { 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 }

Maka, A ∪ B = { 2, 3, 4, 5, 6, 7, 8, 9 }
( A ∪ B )’ = { 10, 11 }
A’ ∩ B’ = { 7, 8, 9, 10, 11 } ∩ { 2, 3, 10, 11 }
              = { 10, 11 }

Jadi, ( A ∪ B )’ = A’ ∩ B’

Diketahui himpunan seperti contoh diatas.
Maka, ( A ∩ B ) = { 4, 5, 6 }
( A ∩ B )’ = { 2, 3, 7, 8, 9, 10, 11 }
A’ ∪ B’ = { 7, 8, 9, 10, 11 } ∪ { 2, 3, 10, 11 }
             = { 2, 3, 7, 8, 9, 10, 11 }

Jadi, ( A ∩ B )’ = A’ ∪ B’

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