Diketahui S={bilangan cacah kurang dari 11} A={x ∣x∈P, x<10, P bilangan prima} B={5, 7, 9} Tentukan g. (A∪B)c∩(A∪B)c

Pertanyaan

Diketahui $\;$
$\style{font-size:14px}{S=\left\{\mathrm{bilangan}\;\mathrm{cacah}\;\mathrm{kurang}\;\mathrm{dari}\;11\right\}}$
$\style{font-size:14px}{A=\left\{x\;\vert x\in\mathrm P,\;x<10,\;\mathrm P\;\mathrm{bilangan}\;\mathrm{prima}\right\}}$
$\style{font-size:14px}{B=\left\{5,\;7,\;9\right\}}$

Tentukan
g. $\style{font-size:14px}{\left(A\cup B\right)^{\mathrm c}\cap\left(A\cup B\right)^{\mathrm c}}$

R. Bella

Master Teacher

Mahasiswa/Alumni UIN Syarif Hidayatullah Jakarta

Jawaban terverifikasi

Jawaban

$\left(A\cup B\right)^{\mathrm c}\cap\left(A\cup B\right)^{\mathrm c}=\begin{array}{rcl}&&\{0,1,4,6,8,9,10\}\end{array}$ .

Pembahasan

Dari soal, diperoleh :

$S=\left\{\mathrm{bilangan}\;\mathrm{cacah}\;\mathrm{kurang}\;\mathrm{dari}\;11\right\}=\{0,1,2,3,4,5,6,7,8,9,10\}$
$A=\left\{x\;\vert x\in\mathrm P,\;x<10,\;\mathrm P\;\mathrm{bilangan}\;\mathrm{prima}\right\}=\{2,3,5,7\}$

Maka, diperoleh perhitungan:

Jadi, $\left(A\cup B\right)^{\mathrm c}\cap\left(A\cup B\right)^{\mathrm c}=\begin{array}{rcl}&&\{0,1,4,6,8,9,10\}\end{array}$ .

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