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

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

In the context of a power set containing a subset,the relation 'is a subset of' $(\subseteq)$ 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:

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

Write the relation $R = \{ (x, x^3) : x \text{ is a prime number less than } 10 \}$ in roster form.