Diketahui himpunan semesta S = {x | x < 15, x e bilangan

a. {3, 5, 7, 11, 13}, b. {9}

Pembahasan

a. A - B^c
Himpunan semesta S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
A = {2, 3, 5, 7, 11, 13} (bilangan prima < 15)
B = {1, 3, 5, 7, 9, 11, 13} (bilangan ganjil < 15)
B^c (komplemen B) = S - B = {2, 4, 6, 8, 10, 12, 14}
A - B^c = {2, 3, 5, 7, 11, 13} - {2, 4, 6, 8, 10, 12, 14} = {3, 5, 7, 11, 13}

b. {A^c - C} ∩ (B - C)
A^c (komplemen A) = S - A = {1, 4, 6, 8, 9, 10, 12, 14}
C = {1, 2, 3, 4, 6, 12} (faktor dari 12)
A^c - C = {1, 4, 6, 8, 9, 10, 12, 14} - {1, 2, 3, 4, 6, 12} = {8, 9, 10, 14}
B - C = {1, 3, 5, 7, 9, 11, 13} - {1, 2, 3, 4, 6, 12} = {5, 7, 9, 11, 13}
{A^c - C} ∩ (B - C) = {8, 9, 10, 14} ∩ {5, 7, 9, 11, 13} = {9}