Let $A$ be the set of even natural numbers that are $< 8$ and $B$ be the set of prime integers that are $< 7$. The number of relations from $A$ to $B$ is:

Let $A = \{1, 2, 3, 4, \ldots, 10\}$ and $B = \{0, 1, 2, 3, 4\}$. The number of elements in the relation $R = \{(a, b) \in A \times A : 2(a - b)^2 + 3(a - b) \in B\}$ is $.........$.

Determine the domain and range of the relation $R$ defined by $R = \{(x, x+5): x \in \{0, 1, 2, 3, 4, 5\}\}$.

$A = \{1, 2, 3, 5\}$ and $B = \{4, 6, 9\}$. Define a relation $R$ from $A$ to $B$ by $R = \{(x, y) : \text{the difference between } x \text{ and } y \text{ is odd}; x \in A, y \in B\}$. Write $R$ in roster form.

Let $n(A) = n$. Then the total number of relations on $A$ is:

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.