If $R = \{(a, b) : b = a - 1, a \in \mathbb{Z}, 5 < a < 9\}$,then the range of $R$ is

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

The number of elements in the relation $R = \{(x, y) : 4x^{2} + y^{2} < 52, x, y \in Z\}$ is

If $A = \{x, y, z\}$ and $B = \{1, 2\}$,then the total number of relations from set $A$ to set $B$ is:

Let $A = \{11, 12, 13\}$ and $B = \{8, 10, 12\}$. $A$ relation $R$ from $A$ to $B$ is defined by $y = x - 3$. Then,find $R^{-1}$.

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 $.........$.