Let $A = \{1, 2, 3, 4, 6\}$. Let $R$ be the relation on $A$ defined by $R = \{(a, b) : a, b \in A, b \text{ is exactly divisible by } a\}$. Write $R$ in roster form.

The set is $A = \{1, 2, 3, 4, 6\}$.
$R$ is defined as the set of ordered pairs $(a, b)$ such that $b$ is divisible by $a$.
We check each element $a \in A$ and find its multiples $b \in A$:
For $a = 1$: $(1, 1), (1, 2), (1, 3), (1, 4), (1, 6)$
For $a = 2$: $(2, 2), (2, 4), (2, 6)$
For $a = 3$: $(3, 3), (3, 6)$
For $a = 4$: $(4, 4)$
For $a = 6$: $(6, 6)$
Thus,the relation $R$ in roster form is:
$R = \{(1, 1), (1, 2), (1, 3), (1, 4), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)\}$