Each of the following open senteces defines a relation R in the natural number N. State whether each relation is symmetric. or not. b. "x is divisible by y"

Pertanyaan

Each of the following open senteces defines a relation $R$ in the natural number $N$ . State whether each relation is symmetric. or not.

b. " $x$ is divisible by $y$ "

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

relasi tersebut bukan merupakan relasi simetris karena jika

habis dibagi

, maka

belum tentu habis dibagi

. Sebagai contoh apabila diambil left parenthesis 4 comma space 2 right parenthesis element of R

tetapi

left parenthesis 2 comma space 4 right parenthesis not an element of R

Pembahasan

Relasi disebut relasi simetris jika untuk setiap left parenthesis a comma space b right parenthesis element of R maka berlaku left parenthesis b comma space a right parenthesis element of R .

Diberikan kalimat terbuka " habis dibagi " yang mendefinisikan relasi dalam bilangan asli . Apabila dinyatakan dalam himpunan pasangan terurut maka

R equals open curly brackets left parenthesis 1 comma 1 right parenthesis comma space left parenthesis 2 comma 2 right parenthesis comma space left parenthesis 4 comma 2 right parenthesis comma space left parenthesis 6 comma 2 right parenthesis comma space left parenthesis 3 comma 3 right parenthesis comma space left parenthesis 6 comma 3 right parenthesis comma space... close curly brackets .

Dengan demikian, relasi tersebut bukan merupakan relasi simetris karena jika habis dibagi , maka belum tentu habis dibagi . Sebagai contoh apabila diambil left parenthesis 4 comma space 2 right parenthesis element of R tetapi left parenthesis 2 comma space 4 right parenthesis not an element of R .

0.0 (0 rating)

Pertanyaan serupa

Each of the following open senteces defines a relation R in the natural number N. State whether each relation is symmetric. or not. c. "x and y are relatively prime"

0.0

Jawaban terverifikasi

Each of the following open senteces defines a relation R in the natural number N. State whether each relation is symmetric. or not. c. "x+y=10"

0.0

Jawaban terverifikasi

Diketahui C={1, 2, 3} dan masing-masing relasi dalam C: R1={(1, 1)} R2={(1, 2)} R3={(1, 1), (3, 2), (2, 3)} R4={(1, 1), (2, 1), (2, 2), (3, 2), (2, 3)} R5=C×C Tuliskan relasi yang merupaka...

3.0

Jawaban terverifikasi

Let L be the set of lines in the euclid and plane and let R be the relation in defined by "x is perpendicular to y". State whether or not is: b. symmetric.

0.0

Jawaban terverifikasi

Each of the following open senteces defines a relation R in the natural number N. State whether each relation is symmetric. or not. a. "x is less than or equal to y"

0.0

Jawaban terverifikasi