Let $A = \{1, 2, 3\}$. The total number of distinct relations that can be defined over $A$ is

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

Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(1,3), (1,5), (2,5)\}$

Relation $R$ on set $N$ is defined as follows:
$R = \{(a, b) : a = b - 2, b > 6\}$. Select the appropriate option.

$A = \{1, 2, 3, 5\}$ 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.