Latihan Matematika Wajib Kelas X Relasi
# 5
Pilgan

Diketahui P={2,3,5} dan Q={2,4,6,8,9,10}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={(2,2),(2,4),(2,6),(2,8),(2,10),(3,6),(3,9),(5,10)}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={(2,4),(2,6),(2,8),(2,10),(3,6),(3,9),(5,10)}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={(2,2),(4,2),(6,2),(8,2),(10,2),(6,3),(9,3),(10,5)}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={(2,2),(4,2),(6,2),(8,2),(10,2),(9,3),(10,5)}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={(4,2),(6,2),(8,2),(10,2),(6,3),(9,3),(10,5)}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={(2,2),(2,4),(2,6),(2,8),(2,10),(3,6),(3,9),(5,10)}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={(2,2),(4,2),(6,2),(8,2),(10,2),(6,3),(9,3),(10,5)}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\}

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