$A$ 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 $A = \{1, 2, 3, \ldots, 10\}$ 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 $A = \{x, y, z\}$ and $B = \{1, 2\}$,then the total number of relations from set $A$ to set $B$ is:

Let the relation $R$ be defined on the set of natural numbers $N$ by $a R b$ if $3 a+2 b=27$. Then $R$ is:

$A = \{1, 2, 3, 5\}$ and $B = \{4, 6, 9\}$. Define a relation $R$ from $A$ to $B$ by $R = \{(x, y) : \text{the difference between } x \text{ and } y \text{ is odd}; x \in A, y \in B\}$. Write $R$ in roster form.

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