Diketahui himpunan-himpunan berikut. S = {x | x < 10, x

a. {1, 2, 3, 4}, b. {0, 1, 2, 3, 4, 6, 8, 9}, c. {3}

Pembahasan

Diketahui:
S = {x | x < 10, x bilangan cacah} = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
P = {x | x < 9, x bilangan ganjil} = {1, 3, 5, 7}
Q = {x | x <= 4, x bilangan asli} = {1, 2, 3, 4}
R = {x | x <= 10, x bilangan kuadrat} = {1, 4, 9}

a. (P ∩ R) ∪ Q
   P ∩ R = {x | x ∈ P dan x ∈ R} = {1, 3, 5, 7} ∩ {1, 4, 9} = {1}
   (P ∩ R) ∪ Q = {1} ∪ {1, 2, 3, 4} = {1, 2, 3, 4}

b. P^C ∪ (R ∪ Q)
   P^C = S - P = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 3, 5, 7} = {0, 2, 4, 6, 8, 9}
   R ∪ Q = {1, 4, 9} ∪ {1, 2, 3, 4} = {1, 2, 3, 4, 9}
   P^C ∪ (R ∪ Q) = {0, 2, 4, 6, 8, 9} ∪ {1, 2, 3, 4, 9} = {0, 1, 2, 3, 4, 6, 8, 9}

c. (Q - R) ∩ P
   Q - R = {x | x ∈ Q dan x ∉ R} = {1, 2, 3, 4} - {1, 4, 9} = {2, 3}
   (Q - R) ∩ P = {2, 3} ∩ {1, 3, 5, 7} = {3}