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

The solution set of $x \equiv 3 \pmod{7}$,where $x \in \mathbb{Z}$,is:

Two finite sets $A$ and $B$ are such that $n(A) = 2$ and $n(B) = 3$. Then the total number of relations from $A$ to $B$ is:

$A$ relation from $P$ to $Q$ is

Let $A = \{1, 2, 3, \ldots, 10\}$ and $R$ be a relation on $A$ such that $R = \{(a, b) : a = 2b + 1\}$. Let $(a_1, a_2), (a_2, a_3), (a_3, a_4), \ldots, (a_k, a_{k+1})$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer $k$,for which such a sequence exists,is equal to:

If $R=\{(x, y): x, y \in Z, x^{2}+3 y^{2} \leq 8\}$ is a relation on the set of integers $Z,$ then the domain of $R^{-1}$ is