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:

Let $A = \{1, 2, 3, 4, 5, 6\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : y = x + 1\}$. Write down the domain,codomain,and range of $R$.

If $n(A) = 2$ and the number of relations from set $A$ to set $B$ is $1024$, then $n(B)$ is

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:

Let $A = \{1, 2, 3, 4\}$,$B = \{1, 5, 9, 11, 15, 16\}$,and $f = \{(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)\}$. Is $f$ a relation from $A$ to $B$? Justify your answer.

$A$ 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