What are the ordered pairs when A = {1, 3, 5, 15, 18} and R be defined by xRy if and only if x|y.

Question

I just wanted to confirm I understand correctly:

When trying to find the pairs for: A = {1, 3, 5, 15, 18} and R be defined by xRy if and only if x|y

First I determine the factors:

x|y 1 is a factor of 3

x|y 1 is a factor of 5

x|y 1 and 3 are factors of 18

x|y 1, 3 and 5 are factors of 15

Therefore the pairs should be as follows: R = {(1,3),(1,5),(1,15),(1,18),(3,15),(3,18),(5,15)}

Is this correct?

Answer 1

Almost correct. Don't forget that $x \mid x$ for all $x \in A$ though! $3$ divides itself, for instance, so $(3,3) \in R$.