Isn't $4$ a multiple of $1$? a question on Relation

Question

List the ordered pairs in the relation $R$ from $A = \{0,1,2,3,4\}$ to $B = \{0,1,2,3\}$, where $(a,b) ∈ R$ if and only if

d) $a|b$.

The solution manual's answer is

$\{ (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 2), (3, 0), (3, 3), (4, O)\}$.

Why $(1,4)$ is not in the $R$?

Answer 1

Because $4\notin B$ (so $(1,4)\notin A\times B$). My question would be why isn't $(0,0)\in R$?

Answer 2

By definition, a relation from $A$ to $B$ is a subset of $A \times B$. In your case, $R$ is defined to be the subset $R := \{(a,b): a \in A, b \in B, a|b \} \subseteq A \times B$. Hence, the second coordinate of each pair $(a,b) \in R$ must be an element of $B = \{0,1,2,3\}$.