Latihan Matematika Wajib Kelas X Relasi
# 2
Pilgan

Diketahui A={3,4,5} dan R={(3,3),(3,4),(3,5),(4,3),(4,4),(5,3),(5,5)}A=\left\{3,4,5\right\}\ \text{dan}\ R=\left\{\left(3,3\right),\left(3,4\right),\left(3,5\right),\left(4,3\right),\left(4,4\right),\left(5,3\right),\left(5,5\right)\right\} .

Maka R dapat disebut sifat relasi ....

A

ekuivalensi

B

simetris

C

transitif

D

invers

E

reflektif

Pembahasan:

Relasi R={(3,3),(3,4),(3,5),(4,3),(4,4),(5,3),(5,5)}R=\left\{\left(3,3\right),\left(3,4\right),\left(3,5\right),\left(4,3\right),\left(4,4\right),\left(5,3\right),\left(5,5\right)\right\} memenuhi sifat relasi:

  • Reflektif, dimana terdapat (3,3),(4,4),(5,5)(3,3),(4,4),(5,5)
  • Simetris dimana terdapat (3,4)∈R\left(3,4\right)\in R dan (4,3)∈R\left(4,3\right)\in R ; (3,5)∈R\left(3,5\right)\in R dan (5,3)∈R\left(5,3\right)\in R
  • Transitif dimana (3,4)∈R\left(3,4\right)\in R dan (4,3)∈R\left(4,3\right)\in R maka (3,3)∈R\left(3,3\right)\in R ; (3,5)∈R\left(3,5\right)\in R dan (5,3)∈R\left(5,3\right)\in R maka (3,3)∈R\left(3,3\right)\in R

Karena Relasi R memiliki 3 sifat, maka relasi R dapat disebur sifat relasi ekuivalen.

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