Bank Soal Matematika SMA Relasi

Soal

Pilgan

Lihat Pembahasan

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

Maka R dapat disebut sifat relasi ....

A

ekuivalensi

B

simetris

C

transitif

D

invers

E

reflektif

Pembahasan:

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

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