# How would I draw the diagram for this relation?

The question I am trying to solve is below. I have proven it is an order but am unsure how to draw the diagram for it. Can someone point me in the right direction?

Let $$A = \{1, 2, 3, 4\}$$, and let $$R$$ be a binary relation on $$A \times A$$ given by: $$((a, b),(c, d)) \in R$$ if and only if $$a$$ divides $$c$$ and $$b$$ divides $$d$$.

What I have so far, on the right track?

Second Level: $$(1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)$$

Bottom Level: $$(1,1)$$

• In the second level just write $(1,2),(1,3),(2,1)$ and $(3,1).$ Don't write $(2,2),$ for example, since you have $(1,2)$ and $(2,1)$ in the middle.
– mfl
Commented Oct 18, 2014 at 23:16

As was noted in the comments, you have far too much in your second level. For instance, $2\mid 4$ and $1\mid 1$, so $\langle 2,1\rangle$ must be below $\langle 4,1\rangle$. On the other hand, we know that there’s nothing between them, because there is no integer $n\{1,2,3,4\}$ such that $2\mid n$, $n\mid 4$, and $n$ is neither $2$ nor $4$.