Let $A = \{1, 2\}$ and $B = \{3, 4\}$. Find the number of relations from $A$ to $B$.

Let $X = \{ 1, 2, 3, 4, 5 \}$ and $Y = \{ 1, 3, 5, 7, 9 \}$. Which of the following is/are relations from $X$ to $Y$?

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 $R$.

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 the number of elements of the sets $A$ and $B$ be $p$ and $q$,respectively. Then,the number of relations from the set $A$ to the set $B$ is

$A$ relation $R$ is defined from $\{2, 3, 4, 5\}$ to $\{3, 6, 7, 10\}$ by $xRy \iff x$ is relatively prime to $y$. Then the domain of $R$ is