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 $A = \{1, 2, 3, \ldots, 10\}$ 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 $A = \{2, 3, 4, 5\}$ 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 $R$?

Let $A = \{1, 2, 3, \ldots, 14\}$. Define a relation $R$ from $A$ to $A$ by $R = \{(x, y) : 3x - y = 0, \text{ where } x, y \in A\}$. Write down its domain,codomain,and range.

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:

Let $R$ be a relation in the set of natural numbers $N$ defined by $R = \{(a, b) : a = b - 2, b > 6\}$. Which of the following is correct?