Let $R$ be the relation in the set $N$ given by $R = \{(a, b) : a = b - 2, b > 6\}$ then which of the following is correct?

The figure shows a relation between the sets $P$ and $Q$. Write this relation in roster form. What is its domain and range?

Let $A = \{1, 2, 3\}$ and $B = \{1, 3, 5\}$. If a relation $R$ from $A$ to $B$ is defined as $R = \{(1, 3), (2, 5), (3, 3)\}$,then find the inverse relation ${R^{ - 1}}$.

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

Define a relation $R$ on the set $N$ of natural numbers by $R = \{(x, y) : y = x + 5, x \text{ is a natural number less than } 4; x, y \in N\}$. Depict this relationship using roster form. Write down the domain and the range.

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