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

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:

The figure shows a relation between the sets $P$ and $Q$. Write this relation in set-builder form. What are its domain and range?

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

Let $R$ be a relation from $N$ to $N$ defined by $R = \{(a, b) : a, b \in N \text{ and } a = b^2\}$. Is the following statement true?
$(a, b) \in R$ implies $(b, a) \in R$

Let $A = \{2, 3, 4, 5\}$ and $B = \{3, 6, 7, 10\}$. $A$ relation $R$ is defined from $A$ to $B$ such that $xRy \iff x$ is relatively prime to $y$. What is the domain of $R$?