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Diketahui A ∪ B = {1, 4, 7, 11, 13, 15} A ∪ C = {1, 5, 7, 10, 13, 15} Maka A ∪ (B ∩ C) = ....
Diketahui
A ∪ B = {1, 4, 7, 11, 13, 15}
A ∪ C = {1, 5, 7, 10, 13, 15}
Maka A ∪ (B ∩ C) = ....
{1, 4, 5, 7, 10, 11, 13, 15}
{1, 4, 5, 7}
{1, 7, 13, 15}
{4, 5, 10, 11}
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I. Sutiawan
Master Teacher
Mahasiswa/Alumni Universitas Pasundan
Pembahasan
Perhatikan bahwa berdasarkan sifat distributif, berlaku bahwa A ∪ (B ∩ C)= (A ∪ B) ∩ (A ∪ C). Karena A ∪ B = {1, 4, 7, 11, 13, 15} dan A ∪ C = {1, 5, 7, 10, 13, 15}, maka A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) = {1, 7, 13, 15}.
Perhatikan bahwa berdasarkan sifat distributif, berlaku bahwa
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).
Karena A ∪ B = {1, 4, 7, 11, 13, 15} dan
A ∪ C = {1, 5, 7, 10, 13, 15}, maka
A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) = {1, 7, 13, 15}.
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