$A$ relation on the set $A = \{x : |x| < 3, x \in Z\}$,where $Z$ is the set of integers,is defined by $R = \{(x, y) : y = |x|, x \neq -1\}$. Then the number of elements in the power set of $R$ is

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 $R$?

Which of the following relations are functions? Give reasons. If it is a function,determine its domain and range.
$\{(1,3), (1,5), (2,5)\}$

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.

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 $A = \{x, y, z\}$ and $B = \{1, 2\}$. Find the number of relations from $A$ to $B$.