Bank Soal Matematika Wajib SMA Relasi

Soal

Pilihan Ganda

Lihat Pembahasan

Diketahui $P=\left\{2,3,5\right\}\ \text{dan}\ Q=\left\{2,4,6,8,9,10\right\}$ dimana relasi antara P dan Q adalah habis membagi. Maka relasi inversnya adalah ....

A

$R^{-1}=\left\{\left(2,2\right),\left(2,4\right),\left(2,6\right),\left(2,8\right),\left(2,10\right),\left(3,6\right),\left(3,9\right),\left(5,10\right)\right\}$

B

$R^{-1}=\left\{\left(2,4\right),\left(2,6\right),\left(2,8\right),\left(2,10\right),\left(3,6\right),\left(3,9\right),\left(5,10\right)\right\}$

C

$R^{-1}=\left\{\left(2,2\right),\left(4,2\right),\left(6,2\right),\left(8,2\right),\left(10,2\right),\left(6,3\right),\left(9,3\right),\left(10,5\right)\right\}$

D

$R^{-1}=\left\{\left(2,2\right),\left(4,2\right),\left(6,2\right),\left(8,2\right),\left(10,2\right),\left(9,3\right),\left(10,5\right)\right\}$

E

$R^{-1}=\left\{\left(4,2\right),\left(6,2\right),\left(8,2\right),\left(10,2\right),\left(6,3\right),\left(9,3\right),\left(10,5\right)\right\}$

Pembahasan:

Relasi P dan Q adalah habis membagi, maka $R=\left\{\left(2,2\right),\left(2,4\right),\left(2,6\right),\left(2,8\right),\left(2,10\right),\left(3,6\right),\left(3,9\right),\left(5,10\right)\right\}$

Relasi inverse adalah kebalikan relasi yang merupakan kebalikan dari R.

Jadi, relasi inversenya adalah $R^{-1}=\left\{\left(2,2\right),\left(4,2\right),\left(6,2\right),\left(8,2\right),\left(10,2\right),\left(6,3\right),\left(9,3\right),\left(10,5\right)\right\}$