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((A ∩ B) ∪ (A ∩ C)) ∪ (A ∩ D) = ....
((A ∩ B) ∪ (A ∩ C)) ∪ (A ∩ D) = ....
((B ∪ D) ∪ C) ∩ A
((B ∪ D) ∪ C) ∪ A
((B ∩ D) ∩ C) ∩ A
((B ∩ D) ∩ C) ∪ A
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I. Sutiawan
Master Teacher
Mahasiswa/Alumni Universitas Pasundan
Pembahasan
Perhatikan bahwa berdasarkan sifat komutatif, asosiatif, dan distributif, berlaku bahwa ((A ∩B) ∪ (A ∩ C)) ∪ (A ∩ D) = (A ∩ (B ∪ C)) ∪ (A ∩ D) = A ∩ ((B ∪ C) ∪ D) = ((B ∪ C) ∪ D) ∩ A = (B ∪ (C ∪ D)) ∩ A = (B ∪ (D ∪ C)) ∩ A = ((B ∪ D) ∪ C) ∩ A
Perhatikan bahwa berdasarkan sifat komutatif, asosiatif, dan distributif, berlaku bahwa
((A ∩ B) ∪ (A ∩ C)) ∪ (A ∩ D)
= (A ∩ (B ∪ C)) ∪ (A ∩ D)
= A ∩ ((B ∪ C) ∪ D)
= ((B ∪ C) ∪ D) ∩ A
= (B ∪ (C ∪ D)) ∩ A
= (B ∪ (D ∪ C)) ∩ A
= ((B ∪ D) ∪ C) ∩ A
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